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<span class="kw">set </span><font color="Maroon" title="c1">cn</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a>;<br/>
<span class="kw">let </span><font color="Maroon" title="c2">L</font> be   <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">K</font> being   <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>  <a href="lattice5.html#NM2" title="LATTICE5:NM.2">Sublattice</a> of <font color="Maroon" title="c2">L</font> st  <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> ,<font color="Olive" title="b1">K</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a>  iff  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">e</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> st <br/>( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font>,<font color="Olive" title="b5">e</font> <a href="zfmisc_1.html#R3" title="ZFMISC_1:pred.3">are_mutually_distinct</a>  &amp; <font color="Olive" title="b1">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b1">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b4">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">e</font> ) )</span><br/>

<a NAME="E1:13"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 1</span>)</span>,2,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T1" onmouseover="rs('yellow_1/T1')" onmouseout="rh()">YELLOW_1:1</a></span>;<br/>
<span class="kw">thus </span><a NAME="E2:13"/>
(  ex <font color="Olive" title="b1">K</font> being   <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>  <a href="lattice5.html#NM2" title="LATTICE5:NM.2">Sublattice</a> of <font color="Maroon" title="c2">L</font> st  <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> ,<font color="Olive" title="b1">K</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a>  implies  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">e</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> st <br/>( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font>,<font color="Olive" title="b5">e</font> <a href="zfmisc_1.html#R3" title="ZFMISC_1:pred.3">are_mutually_distinct</a>  &amp; <font color="Olive" title="b1">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b1">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b4">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">e</font> ) )
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">e</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> st <br/>( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font>,<font color="Olive" title="b5">e</font> <a href="zfmisc_1.html#R3" title="ZFMISC_1:pred.3">are_mutually_distinct</a>  &amp; <font color="Olive" title="b1">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b1">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b4">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">e</font> ) implies  ex <font color="Olive" title="b1">K</font> being   <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>  <a href="lattice5.html#NM2" title="LATTICE5:NM.2">Sublattice</a> of <font color="Maroon" title="c2">L</font> st  <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> ,<font color="Olive" title="b1">K</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a>  )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c3">td</font> = 3 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 2 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">dw</font> = 2 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">t</font> = 3 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">tj</font> = 3 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 1 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">cl</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">z</font> =  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/>
<span class="kw">given </span><font color="Maroon" title="c9">K</font> being   <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>  <a href="lattice5.html#NM2" title="LATTICE5:NM.2">Sublattice</a> of <font color="Maroon" title="c2">L</font><span class="kw"> such that </span><a NAME="E8:13_1"/><span class="lab"><font color="Green" title="E11">A2</font></span>: 
 <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> ,<font color="Maroon" title="c9">K</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">e</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> st <br/>( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font>,<font color="Olive" title="b5">e</font> <a href="zfmisc_1.html#R3" title="ZFMISC_1:pred.3">are_mutually_distinct</a>  &amp; <font color="Olive" title="b1">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b1">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b4">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">e</font> )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c10">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a>,<font color="Maroon" title="c9">K</font><span class="kw"> such that </span><br/><a NAME="E10:13_1"/><span class="lab"><font color="Green" title="E12">A3</font></span>: 
<font color="Maroon" title="c10">f</font> is  <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_1"><span class="lab"><font color="Green" title="E11">A2</font></span></a></span>;<br/>
<a NAME="E11:13_1"/><span class="lab"><font color="Green" title="E13">A4</font></span>: 
 not <font color="Maroon" title="c9">K</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#D38" onmouseover="rs('waybel_0/D38')" onmouseout="rh()">WAYBEL_0:def 38</a></span>;<br/>
<a NAME="E12:13_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A5</font></span>: 
( <font color="Maroon" title="c10">f</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Maroon" title="c10">f</font> is  <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#D38" onmouseover="rs('waybel_0/D38')" onmouseout="rh()">WAYBEL_0:def 38</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">K</font> = <font color="Maroon" title="c9">K</font> as   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c2">L</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#D38" onmouseover="rs('waybel_0/D38')" onmouseout="rh()">WAYBEL_0:def 38</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">ck</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  ;<br/>
<a NAME="E15:13_1"/><span class="lab"><font color="Green" title="E15">A6</font></span>: 
<font color="Maroon" title="c12">ck</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c10">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">g</font> = <font color="Maroon" title="c10">f</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a>,<font color="Maroon" title="c12">ck</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">a</font> = <font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font>, <font color="Maroon" title="c15">b</font> = <font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">td</font>, <font color="Maroon" title="c16">c</font> = <font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">dw</font>, <font color="Maroon" title="c17">d</font> = <font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">tj</font>, <font color="Maroon" title="c18">e</font> = <font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">t</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c11">K</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c19">ck</font> = <font color="Maroon" title="c12">ck</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">cl</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#D13" onmouseover="rs('yellow_0/D13')" onmouseout="rh()">YELLOW_0:def 13</a></span>;<br/>
<a NAME="E19:13_1"/><span class="lab"><font color="Green" title="E16">A7</font></span>: 
<font color="Maroon" title="c15">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c19">ck</font>
 
;<br/>
<a NAME="E20:13_1"/><span class="lab"><font color="Green" title="E17">A8</font></span>: 
<font color="Maroon" title="c16">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c19">ck</font>
 
;<br/>
<a NAME="E21:13_1"/><span class="lab"><font color="Green" title="E18">A9</font></span>: 
<font color="Maroon" title="c18">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c19">ck</font>
 
;<br/>
<a NAME="E22:13_1"/><span class="lab"><font color="Green" title="E19">A10</font></span>: 
<font color="Maroon" title="c17">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c19">ck</font>
 
;<br/>
<a NAME="E23:13_1"/>
<font color="Maroon" title="c14">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c19">ck</font>
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">A</font> = <font color="Maroon" title="c14">a</font>, <font color="Maroon" title="c21">B</font> = <font color="Maroon" title="c15">b</font>, <font color="Maroon" title="c22">C</font> = <font color="Maroon" title="c16">c</font>, <font color="Maroon" title="c23">D</font> = <font color="Maroon" title="c17">d</font>, <font color="Maroon" title="c24">E</font> = <font color="Maroon" title="c18">e</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:13_1"><span class="lab"><font color="Green" title="E16">A7</font></span></a>, <a class="txt" href="#E20:13_1"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="txt" href="#E22:13_1"><span class="lab"><font color="Green" title="E19">A10</font></span></a>, <a class="txt" href="#E21:13_1"><span class="lab"><font color="Green" title="E18">A9</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c20">A</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">d</font>, <font color="Olive" title="b4">e</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> st <br/>( <font color="Maroon" title="c20">A</font>,<font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">c</font>,<font color="Olive" title="b3">d</font>,<font color="Olive" title="b4">e</font> <a href="zfmisc_1.html#R3" title="ZFMISC_1:pred.3">are_mutually_distinct</a>  &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Olive" title="b2">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">c</font> &amp; <font color="Olive" title="b3">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">d</font> &amp; <font color="Olive" title="b1">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Olive" title="b1">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> &amp; <font color="Olive" title="b2">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Olive" title="b1">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">e</font> &amp; <font color="Olive" title="b2">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b3">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">e</font> )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c21">B</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">c</font>, <font color="Olive" title="b2">d</font>, <font color="Olive" title="b3">e</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> st <br/>( <font color="Maroon" title="c20">A</font>,<font color="Maroon" title="c21">B</font>,<font color="Olive" title="b1">c</font>,<font color="Olive" title="b2">d</font>,<font color="Olive" title="b3">e</font> <a href="zfmisc_1.html#R3" title="ZFMISC_1:pred.3">are_mutually_distinct</a>  &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Olive" title="b1">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">c</font> &amp; <font color="Olive" title="b2">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">d</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b2">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Olive" title="b1">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b2">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">e</font> &amp; <font color="Olive" title="b1">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b2">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">e</font> )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c22">C</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">d</font>, <font color="Olive" title="b2">e</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> st <br/>( <font color="Maroon" title="c20">A</font>,<font color="Maroon" title="c21">B</font>,<font color="Maroon" title="c22">C</font>,<font color="Olive" title="b1">d</font>,<font color="Olive" title="b2">e</font> <a href="zfmisc_1.html#R3" title="ZFMISC_1:pred.3">are_mutually_distinct</a>  &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp; <font color="Olive" title="b1">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">d</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">e</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">e</font> )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c23">D</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">e</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> st <br/>( <font color="Maroon" title="c20">A</font>,<font color="Maroon" title="c21">B</font>,<font color="Maroon" title="c22">C</font>,<font color="Maroon" title="c23">D</font>,<font color="Olive" title="b1">e</font> <a href="zfmisc_1.html#R3" title="ZFMISC_1:pred.3">are_mutually_distinct</a>  &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp; <font color="Maroon" title="c23">D</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">e</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">e</font> )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c24">E</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c20">A</font>,<font color="Maroon" title="c21">B</font>,<font color="Maroon" title="c22">C</font>,<font color="Maroon" title="c23">D</font>,<font color="Maroon" title="c24">E</font> <a href="zfmisc_1.html#R3" title="ZFMISC_1:pred.3">are_mutually_distinct</a>  &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp; <font color="Maroon" title="c23">D</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><br/>

<span class="kw">thus </span><a NAME="E25:13_1"/>
<font color="Maroon" title="c20">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:13_1"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="waybel_1.html#D1" onmouseover="rs('waybel_1/D1')" onmouseout="rh()">WAYBEL_1:def 1</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="zfmisc_1.html#D7" onmouseover="rs('zfmisc_1/D7')" onmouseout="rh()">ZFMISC_1:def 7</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c20">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp;  not <font color="Maroon" title="c20">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp;  not <font color="Maroon" title="c20">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp;  not <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp;  not <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp;  not <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp;  not <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp;  not <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp;  not <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp; <font color="Maroon" title="c23">D</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><br/>

<span class="kw">thus </span><a NAME="E26:13_1"/>
<font color="Maroon" title="c20">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c22">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:13_1"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="ref" href="waybel_1.html#D1" onmouseover="rs('waybel_1/D1')" onmouseout="rh()">WAYBEL_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c20">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp;  not <font color="Maroon" title="c20">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp;  not <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp;  not <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp;  not <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp;  not <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp;  not <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp;  not <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp; <font color="Maroon" title="c23">D</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><br/>

<span class="kw">thus </span><a NAME="E27:13_1"/>
<font color="Maroon" title="c20">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">D</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:13_1"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="waybel_1.html#D1" onmouseover="rs('waybel_1/D1')" onmouseout="rh()">WAYBEL_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c20">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp;  not <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp;  not <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp;  not <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp;  not <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp;  not <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp;  not <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp; <font color="Maroon" title="c23">D</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><br/>

<span class="kw">thus </span><a NAME="E28:13_1"/>
<font color="Maroon" title="c20">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">E</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:13_1"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="ref" href="waybel_1.html#D1" onmouseover="rs('waybel_1/D1')" onmouseout="rh()">WAYBEL_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp;  not <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp;  not <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp;  not <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp;  not <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp;  not <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp; <font color="Maroon" title="c23">D</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">dw</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_1"/>
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">dw</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A11</font></span>: 
<font color="Maroon" title="c3">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_1"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="txt" href="#E12:13_1"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="ref" href="waybel_1.html#D1" onmouseover="rs('waybel_1/D1')" onmouseout="rh()">WAYBEL_1:def 1</a></span>;<br/><a NAME="E3:13_1_1"/>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">td</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1_1"><span class="lab"><font color="Green" title="E20">A11</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E30:13_1"/>
<font color="Maroon" title="c21">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c22">C</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp;  not <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp;  not <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp;  not <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp;  not <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp; <font color="Maroon" title="c23">D</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">tj</font></span></a><div class="add"><a NAME="E1:13_1_2"/><span class="lab"><font color="Green" title="E20">A12</font></span>: 
1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><span class="kw">assume </span><a NAME="E2:13_1_2"/><span class="lab"><font color="Green" title="E21">A13</font></span>: 
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">tj</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E3:13_1_2"/>
 not 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">td</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_1"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="txt" href="#E12:13_1"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="txt" href="#E2:13_1_2"><span class="lab"><font color="Green" title="E21">A13</font></span></a>, <a class="txt" href="#E1:13_1_2"><span class="lab"><font color="Green" title="E20">A12</font></span></a>, <a class="ref" href="waybel_1.html#D1" onmouseover="rs('waybel_1/D1')" onmouseout="rh()">WAYBEL_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E32:13_1"/>
<font color="Maroon" title="c21">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">D</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp;  not <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp;  not <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp;  not <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp; <font color="Maroon" title="c23">D</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_3"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">t</font></span></a><div class="add"><a NAME="E1:13_1_3"/><span class="lab"><font color="Green" title="E20">A14</font></span>: 
1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T51" onmouseover="rs('card_1/T51')" onmouseout="rh()">CARD_1:51</a>, <a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</a></span>;<br/><span class="kw">assume </span><a NAME="E2:13_1_3"/><span class="lab"><font color="Green" title="E21">A15</font></span>: 
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">t</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E3:13_1_3"/>
 not 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">td</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_1"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="txt" href="#E12:13_1"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="txt" href="#E2:13_1_3"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="txt" href="#E1:13_1_3"><span class="lab"><font color="Green" title="E20">A14</font></span></a>, <a class="ref" href="waybel_1.html#D1" onmouseover="rs('waybel_1/D1')" onmouseout="rh()">WAYBEL_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E34:13_1"/>
<font color="Maroon" title="c21">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">E</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp;  not <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp;  not <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp; <font color="Maroon" title="c23">D</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_4"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">dw</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">tj</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_4"/>
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">dw</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">tj</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A16</font></span>: 
<font color="Maroon" title="c4">dw</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_1"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="txt" href="#E12:13_1"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="ref" href="waybel_1.html#D1" onmouseover="rs('waybel_1/D1')" onmouseout="rh()">WAYBEL_1:def 1</a></span>;<br/><a NAME="E3:13_1_4"/>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_1_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1_4"><span class="lab"><font color="Green" title="E20">A16</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E36:13_1"/>
<font color="Maroon" title="c22">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">D</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp;  not <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp; <font color="Maroon" title="c23">D</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><br/>

<span class="kw">thus </span><a NAME="E37:13_1"/>
<font color="Maroon" title="c22">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">E</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:13_1"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="ref" href="waybel_1.html#D1" onmouseover="rs('waybel_1/D1')" onmouseout="rh()">WAYBEL_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp; <font color="Maroon" title="c23">D</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_5"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">tj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">t</font></span></a><div class="add"><a NAME="E1:13_1_5"/><span class="lab"><font color="Green" title="E20">A17</font></span>: 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T51" onmouseover="rs('card_1/T51')" onmouseout="rh()">CARD_1:51</a>, <a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</a></span>;<br/><span class="kw">assume </span><a NAME="E2:13_1_5"/><span class="lab"><font color="Green" title="E21">A18</font></span>: 
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">tj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">t</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E3:13_1_5"/>
 not  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_1_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_1"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="txt" href="#E12:13_1"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="txt" href="#E2:13_1_5"><span class="lab"><font color="Green" title="E21">A18</font></span></a>, <a class="txt" href="#E1:13_1_5"><span class="lab"><font color="Green" title="E20">A17</font></span></a>, <a class="ref" href="waybel_1.html#D1" onmouseover="rs('waybel_1/D1')" onmouseout="rh()">WAYBEL_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E39:13_1"/>
<font color="Maroon" title="c23">D</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">E</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp; <font color="Maroon" title="c23">D</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><br/>

<a NAME="E40:13_1"/>
<font color="Maroon" title="c8">z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">td</font>
 
;<br/>
<a NAME="E41:13_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">z</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">td</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/>
<a NAME="E42:13_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c15">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/>
<a NAME="E43:13_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">A</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c21">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T59" onmouseover="rs('yellow_0/T59')" onmouseout="rh()">YELLOW_0:59</a></span>;<br/>
<span class="kw">hence </span><a NAME="E44:13_1"/>
<font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp; <font color="Maroon" title="c23">D</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><br/>

<a NAME="E45:13_1"/>
<font color="Maroon" title="c8">z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">dw</font>
 
;<br/>
<a NAME="E46:13_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">z</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">dw</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/>
<a NAME="E47:13_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c16">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/>
<a NAME="E48:13_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">A</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c22">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T59" onmouseover="rs('yellow_0/T59')" onmouseout="rh()">YELLOW_0:59</a></span>;<br/>
<span class="kw">hence </span><a NAME="E49:13_1"/>
<font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font> &amp; <font color="Maroon" title="c23">D</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><br/>

<a NAME="E50:13_1"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> 2 <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T39" onmouseover="rs('nat_1/T39')" onmouseout="rh()">NAT_1:39</a></span>;<br/>
<a NAME="E51:13_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">dw</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/>
<a NAME="E52:13_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">c</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c18">e</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/>
<a NAME="E53:13_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">C</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c24">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T59" onmouseover="rs('yellow_0/T59')" onmouseout="rh()">YELLOW_0:59</a></span>;<br/>
<span class="kw">hence </span><a NAME="E54:13_1"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c23">D</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><br/>

<a NAME="E55:13_1"/>
<font color="Maroon" title="c6">tj</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/>
<a NAME="E56:13_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">d</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c18">e</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/>
<a NAME="E57:13_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">D</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c24">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T59" onmouseover="rs('yellow_0/T59')" onmouseout="rh()">YELLOW_0:59</a></span>;<br/>
<span class="kw">hence </span><a NAME="E58:13_1"/>
<font color="Maroon" title="c23">D</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><br/>

<span class="kw">thus </span><a NAME="E59:13_1"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font>
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_6"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E20">A19</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_6_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_6_1"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">D</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c22">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T23" onmouseover="rs('yellow_0/T23')" onmouseout="rh()">YELLOW_0:23</a></span>;<br/><a NAME="E3:13_1_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">d</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c16">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>;<br/><a NAME="E4:13_1_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">tj</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/><a NAME="E5:13_1_6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A20</font></span>: 
<font color="Maroon" title="c6">tj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><a NAME="E6:13_1_6_1"/>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><a NAME="E7:13_1_6_1"/><span class="kw">then </span>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1_6_1"><span class="lab"><font color="Green" title="E21">A20</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E8:13_1_6_1"/>
contradiction
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E21">A21</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_6_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_6_2"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_6_2"/><span class="kw">then </span>
<font color="Maroon" title="c24">E</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c22">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T23" onmouseover="rs('yellow_0/T23')" onmouseout="rh()">YELLOW_0:23</a></span>;<br/><a NAME="E3:13_1_6_2"/><span class="kw">then </span>
<font color="Maroon" title="c18">e</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c16">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>;<br/><a NAME="E4:13_1_6_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">t</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/><a NAME="E5:13_1_6_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A22</font></span>: 
<font color="Maroon" title="c5">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><a NAME="E6:13_1_6_2"/>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T51" onmouseover="rs('card_1/T51')" onmouseout="rh()">CARD_1:51</a>, <a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</a></span>;<br/><a NAME="E7:13_1_6_2"/><span class="kw">then </span>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1_6_2"><span class="lab"><font color="Green" title="E22">A22</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E8:13_1_6_2"/>
contradiction
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E22">A23</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_6_3"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_6_3"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_6_3"/><span class="kw">then </span>
<font color="Maroon" title="c21">B</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c22">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_1_6_3"/><span class="kw">then </span>
<font color="Maroon" title="c15">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c16">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>;<br/><a NAME="E4:13_1_6_3"/><span class="kw">then </span>
<font color="Maroon" title="c3">td</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/><a NAME="E5:13_1_6_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A24</font></span>: 
<font color="Maroon" title="c3">td</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><a NAME="E6:13_1_6_3"/>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">td</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><a NAME="E7:13_1_6_3"/><span class="kw">then </span>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1_6_3"><span class="lab"><font color="Green" title="E23">A24</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E8:13_1_6_3"/>
contradiction
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E23">A25</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_6_4"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_6_4"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_6_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">C</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c21">B</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_1_6_4"/><span class="kw">then </span>
<font color="Maroon" title="c16">c</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c15">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>;<br/><a NAME="E4:13_1_6_4"/><span class="kw">then </span>
<font color="Maroon" title="c4">dw</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">td</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/><a NAME="E5:13_1_6_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A26</font></span>: 
<font color="Maroon" title="c4">dw</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">td</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><a NAME="E6:13_1_6_4"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T50" onmouseover="rs('card_1/T50')" onmouseout="rh()">CARD_1:50</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E7:13_1_6_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1_6_4"><span class="lab"><font color="Green" title="E24">A26</font></span></a>, <a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E5:13_1_6"/>
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c21">B</font>,<font color="Maroon" title="c22">C</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T21" onmouseover="rs('yellow_0/T21')" onmouseout="rh()">YELLOW_0:21</a></span>;<br/>
<a NAME="E6:13_1_6"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c21">B</font>,<font color="Maroon" title="c22">C</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#D16" onmouseover="rs('yellow_0/D16')" onmouseout="rh()">YELLOW_0:def 16</a></span>;<br/>
<a NAME="E7:13_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c10">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_1"><span class="lab"><font color="Green" title="E15">A6</font></span></a>, <a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/>
<a NAME="E8:13_1_6"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c10">f</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:13_1_6"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E3:13_1_6"><span class="lab"><font color="Green" title="E22">A23</font></span></a>, <a class="txt" href="#E4:13_1_6"><span class="lab"><font color="Green" title="E23">A25</font></span></a>, <a class="txt" href="#E1:13_1_6"><span class="lab"><font color="Green" title="E20">A19</font></span></a>, <a class="txt" href="#E2:13_1_6"><span class="lab"><font color="Green" title="E21">A21</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<a NAME="E60:13_1"/>
<font color="Maroon" title="c3">td</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">tj</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="yellow11.html#E5"><span class="lab"><font color="Green" title="E4">Lm1</font></span></a>, <a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/>
<a NAME="E61:13_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c17">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/>
<a NAME="E62:13_1"/><span class="kw">then </span>
<font color="Maroon" title="c21">B</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c23">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T59" onmouseover="rs('yellow_0/T59')" onmouseout="rh()">YELLOW_0:59</a></span>;<br/>
<span class="kw">hence </span><a NAME="E63:13_1"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><br/>

<span class="kw">thus </span><a NAME="E64:13_1"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font>
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font> )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_7"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E20">A27</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_7_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_7_1"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_7_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">D</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c22">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T23" onmouseover="rs('yellow_0/T23')" onmouseout="rh()">YELLOW_0:23</a></span>;<br/><a NAME="E3:13_1_7_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">d</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c16">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>;<br/><a NAME="E4:13_1_7_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">tj</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/><a NAME="E5:13_1_7_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A28</font></span>: 
<font color="Maroon" title="c6">tj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><a NAME="E6:13_1_7_1"/>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><a NAME="E7:13_1_7_1"/><span class="kw">then </span>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1_7_1"><span class="lab"><font color="Green" title="E21">A28</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E8:13_1_7_1"/>
contradiction
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E21">A29</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_7_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_7_2"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c24">E</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c22">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T23" onmouseover="rs('yellow_0/T23')" onmouseout="rh()">YELLOW_0:23</a></span>;<br/><a NAME="E3:13_1_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c18">e</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c16">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>;<br/><a NAME="E4:13_1_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">t</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/><a NAME="E5:13_1_7_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A30</font></span>: 
<font color="Maroon" title="c5">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><a NAME="E6:13_1_7_2"/>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T51" onmouseover="rs('card_1/T51')" onmouseout="rh()">CARD_1:51</a>, <a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</a></span>;<br/><a NAME="E7:13_1_7_2"/><span class="kw">then </span>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1_7_2"><span class="lab"><font color="Green" title="E22">A30</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E8:13_1_7_2"/>
contradiction
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E22">A31</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_7_3"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_7_3"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_7_3"/><span class="kw">then </span>
<font color="Maroon" title="c21">B</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c22">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T23" onmouseover="rs('yellow_0/T23')" onmouseout="rh()">YELLOW_0:23</a></span>;<br/><a NAME="E3:13_1_7_3"/><span class="kw">then </span>
<font color="Maroon" title="c15">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c16">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>;<br/><a NAME="E4:13_1_7_3"/><span class="kw">then </span>
<font color="Maroon" title="c3">td</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/><a NAME="E5:13_1_7_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A32</font></span>: 
<font color="Maroon" title="c3">td</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><a NAME="E6:13_1_7_3"/>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">td</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><a NAME="E7:13_1_7_3"/><span class="kw">then </span>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1_7_3"><span class="lab"><font color="Green" title="E23">A32</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E8:13_1_7_3"/>
contradiction
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E23">A33</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_7_4"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_7_4"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_7_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">C</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c23">D</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_1_7_4"/><span class="kw">then </span>
<font color="Maroon" title="c16">c</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c17">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>;<br/><a NAME="E4:13_1_7_4"/><span class="kw">then </span>
<font color="Maroon" title="c4">dw</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/><a NAME="E5:13_1_7_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A34</font></span>: 
<font color="Maroon" title="c4">dw</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><a NAME="E6:13_1_7_4"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T50" onmouseover="rs('card_1/T50')" onmouseout="rh()">CARD_1:50</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E7:13_1_7_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1_7_4"><span class="lab"><font color="Green" title="E24">A34</font></span></a>, <a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E5:13_1_7"/>
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c22">C</font>,<font color="Maroon" title="c23">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T21" onmouseover="rs('yellow_0/T21')" onmouseout="rh()">YELLOW_0:21</a></span>;<br/>
<a NAME="E6:13_1_7"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c22">C</font>,<font color="Maroon" title="c23">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#D16" onmouseover="rs('yellow_0/D16')" onmouseout="rh()">YELLOW_0:def 16</a></span>;<br/>
<a NAME="E7:13_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c10">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_1"><span class="lab"><font color="Green" title="E15">A6</font></span></a>, <a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/>
<a NAME="E8:13_1_7"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c10">f</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:13_1_7"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E3:13_1_7"><span class="lab"><font color="Green" title="E22">A31</font></span></a>, <a class="txt" href="#E4:13_1_7"><span class="lab"><font color="Green" title="E23">A33</font></span></a>, <a class="txt" href="#E1:13_1_7"><span class="lab"><font color="Green" title="E20">A27</font></span></a>, <a class="txt" href="#E2:13_1_7"><span class="lab"><font color="Green" title="E21">A29</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E65:13_1"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font>
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font></span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_8"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E20">A35</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_8_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_8_1"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_8_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">C</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c21">B</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T24" onmouseover="rs('yellow_0/T24')" onmouseout="rh()">YELLOW_0:24</a></span>;<br/><a NAME="E3:13_1_8_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">c</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c15">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>;<br/><a NAME="E4:13_1_8_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">dw</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c3">td</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/><a NAME="E5:13_1_8_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A36</font></span>: 
<font color="Maroon" title="c3">td</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><a NAME="E6:13_1_8_1"/>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">td</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><a NAME="E7:13_1_8_1"/><span class="kw">then </span>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1_8_1"><span class="lab"><font color="Green" title="E21">A36</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E8:13_1_8_1"/>
contradiction
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E21">A37</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_8_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_8_2"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_8_2"/><span class="kw">then </span>
<font color="Maroon" title="c23">D</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c22">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T22" onmouseover="rs('yellow_0/T22')" onmouseout="rh()">YELLOW_0:22</a></span>;<br/><a NAME="E3:13_1_8_2"/><span class="kw">then </span>
<font color="Maroon" title="c17">d</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c16">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>;<br/><a NAME="E4:13_1_8_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">tj</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/><a NAME="E5:13_1_8_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A38</font></span>: 
<font color="Maroon" title="c4">dw</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><a NAME="E6:13_1_8_2"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T50" onmouseover="rs('card_1/T50')" onmouseout="rh()">CARD_1:50</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E7:13_1_8_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1_8_2"><span class="lab"><font color="Green" title="E22">A38</font></span></a>, <a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E22">A39</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_8_3"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_8_3"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_8_3"/><span class="kw">then </span>
<font color="Maroon" title="c21">B</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c22">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T24" onmouseover="rs('yellow_0/T24')" onmouseout="rh()">YELLOW_0:24</a></span>;<br/><a NAME="E3:13_1_8_3"/><span class="kw">then </span>
<font color="Maroon" title="c15">b</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c16">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>;<br/><a NAME="E4:13_1_8_3"/><span class="kw">then </span>
<font color="Maroon" title="c3">td</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/><a NAME="E5:13_1_8_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A40</font></span>: 
<font color="Maroon" title="c4">dw</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">td</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><a NAME="E6:13_1_8_3"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T50" onmouseover="rs('card_1/T50')" onmouseout="rh()">CARD_1:50</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E7:13_1_8_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1_8_3"><span class="lab"><font color="Green" title="E23">A40</font></span></a>, <a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E23">A41</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_8_4"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_8_4"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_8_4"/><span class="kw">then </span>
<font color="Maroon" title="c20">A</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c22">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T22" onmouseover="rs('yellow_0/T22')" onmouseout="rh()">YELLOW_0:22</a></span>;<br/><a NAME="E3:13_1_8_4"/><span class="kw">then </span>
<font color="Maroon" title="c14">a</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c16">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>;<br/><a NAME="E4:13_1_8_4"/><span class="kw">then </span>
<font color="Maroon" title="c8">z</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/><a NAME="E5:13_1_8_4"/><span class="kw">then </span>
<font color="Maroon" title="c4">dw</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><span class="kw">hence </span><a NAME="E6:13_1_8_4"/>
contradiction
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E5:13_1_8"/>
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c21">B</font>,<font color="Maroon" title="c22">C</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T20" onmouseover="rs('yellow_0/T20')" onmouseout="rh()">YELLOW_0:20</a></span>;<br/>
<a NAME="E6:13_1_8"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c21">B</font>,<font color="Maroon" title="c22">C</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#D17" onmouseover="rs('yellow_0/D17')" onmouseout="rh()">YELLOW_0:def 17</a></span>;<br/>
<a NAME="E7:13_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c10">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_1"><span class="lab"><font color="Green" title="E15">A6</font></span></a>, <a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/>
<a NAME="E8:13_1_8"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c10">f</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:13_1_8"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E3:13_1_8"><span class="lab"><font color="Green" title="E22">A39</font></span></a>, <a class="txt" href="#E1:13_1_8"><span class="lab"><font color="Green" title="E20">A35</font></span></a>, <a class="txt" href="#E2:13_1_8"><span class="lab"><font color="Green" title="E21">A37</font></span></a>, <a class="txt" href="#E4:13_1_8"><span class="lab"><font color="Green" title="E23">A41</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E66:13_1"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font>
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_9"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E20">A42</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_9_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_9_1"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_9_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">D</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c22">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T22" onmouseover="rs('yellow_0/T22')" onmouseout="rh()">YELLOW_0:22</a></span>;<br/><a NAME="E3:13_1_9_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">d</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c16">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>;<br/><a NAME="E4:13_1_9_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">tj</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/><a NAME="E5:13_1_9_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A43</font></span>: 
<font color="Maroon" title="c4">dw</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><a NAME="E6:13_1_9_1"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T50" onmouseover="rs('card_1/T50')" onmouseout="rh()">CARD_1:50</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E7:13_1_9_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1_9_1"><span class="lab"><font color="Green" title="E21">A43</font></span></a>, <a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E21">A44</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_9_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_9_2"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_9_2"/><span class="kw">then </span>
<font color="Maroon" title="c22">C</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c23">D</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T24" onmouseover="rs('yellow_0/T24')" onmouseout="rh()">YELLOW_0:24</a></span>;<br/><a NAME="E3:13_1_9_2"/><span class="kw">then </span>
<font color="Maroon" title="c16">c</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c17">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>;<br/><a NAME="E4:13_1_9_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">dw</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c6">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/><a NAME="E5:13_1_9_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A45</font></span>: 
<font color="Maroon" title="c6">tj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><a NAME="E6:13_1_9_2"/>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E7:13_1_9_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1_9_2"><span class="lab"><font color="Green" title="E22">A45</font></span></a>, <a class="ref" href="card_1.html#T50" onmouseover="rs('card_1/T50')" onmouseout="rh()">CARD_1:50</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E22">A46</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_9_3"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_9_3"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_9_3"/><span class="kw">then </span>
<font color="Maroon" title="c21">B</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c22">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T22" onmouseover="rs('yellow_0/T22')" onmouseout="rh()">YELLOW_0:22</a></span>;<br/><a NAME="E3:13_1_9_3"/><span class="kw">then </span>
<font color="Maroon" title="c15">b</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c16">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>;<br/><a NAME="E4:13_1_9_3"/><span class="kw">then </span>
<font color="Maroon" title="c3">td</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/><a NAME="E5:13_1_9_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A47</font></span>: 
<font color="Maroon" title="c4">dw</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">td</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><a NAME="E6:13_1_9_3"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T50" onmouseover="rs('card_1/T50')" onmouseout="rh()">CARD_1:50</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E7:13_1_9_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1_9_3"><span class="lab"><font color="Green" title="E23">A47</font></span></a>, <a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E23">A48</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_1_9_4"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_9_4"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_9_4"/><span class="kw">then </span>
<font color="Maroon" title="c20">A</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c22">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T22" onmouseover="rs('yellow_0/T22')" onmouseout="rh()">YELLOW_0:22</a></span>;<br/><a NAME="E3:13_1_9_4"/><span class="kw">then </span>
<font color="Maroon" title="c14">a</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c16">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>;<br/><a NAME="E4:13_1_9_4"/><span class="kw">then </span>
<font color="Maroon" title="c8">z</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c4">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>;<br/><a NAME="E5:13_1_9_4"/><span class="kw">then </span>
<font color="Maroon" title="c4">dw</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><span class="kw">hence </span><a NAME="E6:13_1_9_4"/>
contradiction
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E5:13_1_9"/>
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c22">C</font>,<font color="Maroon" title="c23">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T20" onmouseover="rs('yellow_0/T20')" onmouseout="rh()">YELLOW_0:20</a></span>;<br/>
<a NAME="E6:13_1_9"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c22">C</font>,<font color="Maroon" title="c23">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#D17" onmouseover="rs('yellow_0/D17')" onmouseout="rh()">YELLOW_0:def 17</a></span>;<br/>
<a NAME="E7:13_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c10">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_1"><span class="lab"><font color="Green" title="E15">A6</font></span></a>, <a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/>
<a NAME="E8:13_1_9"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c10">f</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:13_1_9"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E3:13_1_9"><span class="lab"><font color="Green" title="E22">A46</font></span></a>, <a class="txt" href="#E2:13_1_9"><span class="lab"><font color="Green" title="E21">A44</font></span></a>, <a class="txt" href="#E1:13_1_9"><span class="lab"><font color="Green" title="E20">A42</font></span></a>, <a class="txt" href="#E4:13_1_9"><span class="lab"><font color="Green" title="E23">A48</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E3:13"/>
(  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">e</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> st <br/>( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font>,<font color="Olive" title="b5">e</font> <a href="zfmisc_1.html#R3" title="ZFMISC_1:pred.3">are_mutually_distinct</a>  &amp; <font color="Olive" title="b1">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b1">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b4">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">e</font> ) implies  ex <font color="Olive" title="b1">K</font> being   <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>  <a href="lattice5.html#NM2" title="LATTICE5:NM.2">Sublattice</a> of <font color="Maroon" title="c2">L</font> st  <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> ,<font color="Olive" title="b1">K</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a>  )
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">given </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c6">d</font>, <font color="Maroon" title="c7">e</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font><span class="kw"> such that </span><a NAME="E2:13_2"/><span class="lab"><font color="Green" title="E11">AAA</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c7">e</font> <a href="zfmisc_1.html#R3" title="ZFMISC_1:pred.3">are_mutually_distinct</a> 
 <span class="kw">and </span><br/><a NAME="E3:13_2"/><span class="lab"><font color="Green" title="E12">A59</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">and </span><br/><a NAME="E4:13_2"/><span class="lab"><font color="Green" title="E13">A60</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">and </span><br/><a NAME="E5:13_2"/><span class="lab"><font color="Green" title="E14">A61</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">and </span><br/><a NAME="E6:13_2"/><span class="lab"><font color="Green" title="E15">A62</font></span>: 
<font color="Maroon" title="c6">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">and </span><br/><a NAME="E7:13_2"/><span class="lab"><font color="Green" title="E16">A63</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">and </span><br/><a NAME="E8:13_2"/><span class="lab"><font color="Green" title="E17">A64</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">and </span><br/><a NAME="E9:13_2"/><span class="lab"><font color="Green" title="E18">A65</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">and </span><br/><a NAME="E10:13_2"/><span class="lab"><font color="Green" title="E19">A66</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">and </span><br/><a NAME="E11:13_2"/><span class="lab"><font color="Green" title="E20">A67</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">K</font> being   <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>  <a href="lattice5.html#NM2" title="LATTICE5:NM.2">Sublattice</a> of <font color="Maroon" title="c2">L</font> st  <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> ,<font color="Olive" title="b1">K</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c8">ck</font> = <span class="p1"><a href="domain_1.html#K10" title="DOMAIN_1:func.10">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c7">e</font></span><a href="domain_1.html#K10" title="DOMAIN_1:func.10">}</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">ck</font> = <span class="p1"><a href="domain_1.html#K10" title="DOMAIN_1:func.10">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c7">e</font></span><a href="domain_1.html#K10" title="DOMAIN_1:func.10">}</a></span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">L</font> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">K</font> =  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font>;<br/>
<a NAME="E13:13_2"/><span class="lab"><font color="Green" title="E21">A68</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">ck</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#D15" onmouseover="rs('yellow_0/D15')" onmouseout="rh()">YELLOW_0:def 15</a></span>;<br/>
<a NAME="E14:13_2"/><span class="lab"><font color="Green" title="E22">A69</font></span>: 
 <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font> is  <a href="yellow_0.html#V5" title="YELLOW_0:attr.5">meet-inheriting</a> 
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c12">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="yellow_0.html#D16" onmouseover="rs('yellow_0/D16')" onmouseout="rh()">YELLOW_0:def 16</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c11">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span> or  not <font color="Maroon" title="c12">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span> or  not  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font> or  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:13_2_1"/><span class="lab"><font color="Green" title="E23">A70</font></span>: 
<font color="Maroon" title="c11">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:13_2_1"/><span class="lab"><font color="Green" title="E24">A71</font></span>: 
<font color="Maroon" title="c12">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:13_2_1"/>
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:13_2_1_1"/>
( ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="txt" href="#E1:13_2_1"><span class="lab"><font color="Green" title="E23">A70</font></span></a>, <a class="txt" href="#E2:13_2_1"><span class="lab"><font color="Green" title="E24">A71</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_1"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_1"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><a NAME="E3:13_2_1_1_1"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_5.html#T2" onmouseover="rs('yellow_5/T2')" onmouseout="rh()">YELLOW_5:2</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_1_1_1"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_2"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_2"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_1_1_2"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2"><span class="lab"><font color="Green" title="E12">A59</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_3"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_3"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_1_1_3"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13_2"><span class="lab"><font color="Green" title="E13">A60</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_4"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_4"/><span class="lab"><font color="Green" title="E25">A72</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_4"/><span class="lab"><font color="Green" title="E26">A73</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_1_1_4"/>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2"><span class="lab"><font color="Green" title="E12">A59</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_1_1_4"><span class="lab"><font color="Green" title="E26">A73</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E5:13_2_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E6:13_2_1_1_4"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_1_1_4"><span class="lab"><font color="Green" title="E25">A72</font></span></a>, <a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E7:13_2_1_1_4"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_5"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_5"/><span class="lab"><font color="Green" title="E25">A74</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_5"/><span class="lab"><font color="Green" title="E26">A75</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2"><span class="lab"><font color="Green" title="E14">A61</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_1_1_5"/>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13_2"><span class="lab"><font color="Green" title="E13">A60</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_1_1_5"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_1_1_5"><span class="lab"><font color="Green" title="E26">A75</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E5:13_2_1_1_5"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E6:13_2_1_1_5"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_1_1_5"><span class="lab"><font color="Green" title="E25">A74</font></span></a>, <a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E7:13_2_1_1_5"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_6"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_6"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_6"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_1_1_6"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2"><span class="lab"><font color="Green" title="E12">A59</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_7"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_7"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_7"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><a NAME="E3:13_2_1_1_7"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_5.html#T2" onmouseover="rs('yellow_5/T2')" onmouseout="rh()">YELLOW_5:2</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_1_1_7"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_8"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_8"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_8"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_1_1_8"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:13_2"><span class="lab"><font color="Green" title="E16">A63</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_9"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_9"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_9"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_1_1_9"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_10"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_10"/><span class="lab"><font color="Green" title="E25">A76</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_10"/><span class="lab"><font color="Green" title="E26">A77</font></span>: 
<font color="Maroon" title="c6">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_2"><span class="lab"><font color="Green" title="E15">A62</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_1_1_10"/>
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_1_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_1_1_10"><span class="lab"><font color="Green" title="E26">A77</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E5:13_2_1_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E6:13_2_1_1_10"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_1_1_10"><span class="lab"><font color="Green" title="E25">A76</font></span></a>, <a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E7:13_2_1_1_10"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_11"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_11"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_11"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_1_1_11"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13_2"><span class="lab"><font color="Green" title="E13">A60</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_12"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_12"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_12"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_1_1_12"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:13_2"><span class="lab"><font color="Green" title="E16">A63</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_13"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_13"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_13"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><a NAME="E3:13_2_1_1_13"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_5.html#T2" onmouseover="rs('yellow_5/T2')" onmouseout="rh()">YELLOW_5:2</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_1_1_13"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_14"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_14"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_14"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_1_1_14"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13_2"><span class="lab"><font color="Green" title="E18">A65</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_15"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_15"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_15"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_1_1_15"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2"><span class="lab"><font color="Green" title="E14">A61</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_16"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_16"/><span class="lab"><font color="Green" title="E25">A78</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_16"/><span class="lab"><font color="Green" title="E26">A79</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_1_1_16"/>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2"><span class="lab"><font color="Green" title="E12">A59</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_1_1_16"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_1_1_16"><span class="lab"><font color="Green" title="E26">A79</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E5:13_2_1_1_16"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E6:13_2_1_1_16"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_1_1_16"><span class="lab"><font color="Green" title="E25">A78</font></span></a>, <a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E7:13_2_1_1_16"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_17"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_17"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_17"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_1_1_17"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_18"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_18"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_18"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_1_1_18"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13_2"><span class="lab"><font color="Green" title="E18">A65</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_19"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_19"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_19"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><a NAME="E3:13_2_1_1_19"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_5.html#T2" onmouseover="rs('yellow_5/T2')" onmouseout="rh()">YELLOW_5:2</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_1_1_19"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_20"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_20"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_20"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_1_1_20"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_2"><span class="lab"><font color="Green" title="E15">A62</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_21"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_21"/><span class="lab"><font color="Green" title="E25">A80</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_21"/><span class="lab"><font color="Green" title="E26">A81</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2"><span class="lab"><font color="Green" title="E14">A61</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_1_1_21"/>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13_2"><span class="lab"><font color="Green" title="E13">A60</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_1_1_21"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_1_1_21"><span class="lab"><font color="Green" title="E26">A81</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E5:13_2_1_1_21"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E6:13_2_1_1_21"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_1_1_21"><span class="lab"><font color="Green" title="E25">A80</font></span></a>, <a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E7:13_2_1_1_21"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_22"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_22"/><span class="lab"><font color="Green" title="E25">A82</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_22"/><span class="lab"><font color="Green" title="E26">A83</font></span>: 
<font color="Maroon" title="c6">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_2"><span class="lab"><font color="Green" title="E15">A62</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_1_1_22"/>
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_1_1_22"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_1_1_22"><span class="lab"><font color="Green" title="E26">A83</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E5:13_2_1_1_22"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E6:13_2_1_1_22"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_1_1_22"><span class="lab"><font color="Green" title="E25">A82</font></span></a>, <a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E7:13_2_1_1_22"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_23"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_23"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_23"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_1_1_23"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2"><span class="lab"><font color="Green" title="E14">A61</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_24"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_24"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_24"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_1_1_24"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_2"><span class="lab"><font color="Green" title="E15">A62</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_1_1_25"><span class="kw">suppose </span></a><a NAME="E1:13_2_1_1_25"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_1_1_25"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T40" onmouseover="rs('yellow_0/T40')" onmouseout="rh()">YELLOW_0:40</a></span>;<br/><a NAME="E3:13_2_1_1_25"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_5.html#T2" onmouseover="rs('yellow_5/T2')" onmouseout="rh()">YELLOW_5:2</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_1_1_25"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<a NAME="E15:13_2"/>
 <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font> is  <a href="yellow_0.html#V6" title="YELLOW_0:attr.6">join-inheriting</a> 
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c12">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="yellow_0.html#D17" onmouseover="rs('yellow_0/D17')" onmouseout="rh()">YELLOW_0:def 17</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c11">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span> or  not <font color="Maroon" title="c12">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span> or  not  <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font> or  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:13_2_2"/><span class="lab"><font color="Green" title="E23">A84</font></span>: 
<font color="Maroon" title="c11">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:13_2_2"/><span class="lab"><font color="Green" title="E24">A85</font></span>: 
<font color="Maroon" title="c12">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:13_2_2"/>
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:13_2_2_1"/>
( ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="txt" href="#E1:13_2_2"><span class="lab"><font color="Green" title="E23">A84</font></span></a>, <a class="txt" href="#E2:13_2_2"><span class="lab"><font color="Green" title="E24">A85</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_1"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_1"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><a NAME="E3:13_2_2_1_1"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_5.html#T1" onmouseover="rs('yellow_5/T1')" onmouseout="rh()">YELLOW_5:1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_2_1_1"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_2"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">x</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2"><span class="lab"><font color="Green" title="E12">A59</font></span></a>, <a class="ref" href="yellow11.html#T5" target="_self" onmouseover="rs('yellow11/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E3:13_2_2_1_2"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_2_1_2"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_3"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_3"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c11">x</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13_2"><span class="lab"><font color="Green" title="E13">A60</font></span></a>, <a class="ref" href="yellow11.html#T5" target="_self" onmouseover="rs('yellow11/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E3:13_2_2_1_3"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_2_1_3"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_4"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_4"/><span class="lab"><font color="Green" title="E25">A86</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_4"/><span class="lab"><font color="Green" title="E26">A87</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_2_1_4"/>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2"><span class="lab"><font color="Green" title="E12">A59</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_2_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_2_1_4"><span class="lab"><font color="Green" title="E26">A87</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E5:13_2_2_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E6:13_2_2_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T5" target="_self" onmouseover="rs('yellow11/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E7:13_2_2_1_4"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_2_1_4"><span class="lab"><font color="Green" title="E25">A86</font></span></a>, <a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E8:13_2_2_1_4"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_5"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_5"/><span class="lab"><font color="Green" title="E25">A88</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_5"/><span class="lab"><font color="Green" title="E26">A89</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2"><span class="lab"><font color="Green" title="E14">A61</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_2_1_5"/>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13_2"><span class="lab"><font color="Green" title="E13">A60</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_2_1_5"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_2_1_5"><span class="lab"><font color="Green" title="E26">A89</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E5:13_2_2_1_5"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E6:13_2_2_1_5"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T5" target="_self" onmouseover="rs('yellow11/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E7:13_2_2_1_5"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_2_1_5"><span class="lab"><font color="Green" title="E25">A88</font></span></a>, <a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E8:13_2_2_1_5"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_6"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_6"/><span class="lab"><font color="Green" title="E25">A90</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_6"/>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2"><span class="lab"><font color="Green" title="E12">A59</font></span></a>, <a class="ref" href="yellow11.html#T5" target="_self" onmouseover="rs('yellow11/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E3:13_2_2_1_6"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_2_1_6"><span class="lab"><font color="Green" title="E25">A90</font></span></a>, <a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_2_1_6"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_7"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_7"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_7"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><a NAME="E3:13_2_2_1_7"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_5.html#T1" onmouseover="rs('yellow_5/T1')" onmouseout="rh()">YELLOW_5:1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_2_1_7"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_8"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_8"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_8"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_2_1_8"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_2"><span class="lab"><font color="Green" title="E19">A66</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_9"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_9"/><span class="lab"><font color="Green" title="E25">A91</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_9"/>
<font color="Maroon" title="c4">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="ref" href="yellow11.html#T5" target="_self" onmouseover="rs('yellow11/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E3:13_2_2_1_9"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_2_1_9"><span class="lab"><font color="Green" title="E25">A91</font></span></a>, <a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_2_1_9"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_10"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_10"/><span class="lab"><font color="Green" title="E25">A92</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_10"/><span class="lab"><font color="Green" title="E26">A93</font></span>: 
<font color="Maroon" title="c6">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_2"><span class="lab"><font color="Green" title="E15">A62</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_2_1_10"/>
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_2_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_2_1_10"><span class="lab"><font color="Green" title="E26">A93</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E5:13_2_2_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E6:13_2_2_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T5" target="_self" onmouseover="rs('yellow11/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E7:13_2_2_1_10"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_2_1_10"><span class="lab"><font color="Green" title="E25">A92</font></span></a>, <a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E8:13_2_2_1_10"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_11"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_11"/><span class="lab"><font color="Green" title="E25">A94</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_11"/>
<font color="Maroon" title="c5">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13_2"><span class="lab"><font color="Green" title="E13">A60</font></span></a>, <a class="ref" href="yellow11.html#T5" target="_self" onmouseover="rs('yellow11/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E3:13_2_2_1_11"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_2_1_11"><span class="lab"><font color="Green" title="E25">A94</font></span></a>, <a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_2_1_11"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_12"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_12"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_12"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_2_1_12"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_2"><span class="lab"><font color="Green" title="E19">A66</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_13"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_13"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_13"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><a NAME="E3:13_2_2_1_13"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_5.html#T1" onmouseover="rs('yellow_5/T1')" onmouseout="rh()">YELLOW_5:1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_2_1_13"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_14"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_14"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_14"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_2_1_14"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_2"><span class="lab"><font color="Green" title="E20">A67</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_15"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_15"/><span class="lab"><font color="Green" title="E25">A95</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_15"/>
<font color="Maroon" title="c5">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2"><span class="lab"><font color="Green" title="E14">A61</font></span></a>, <a class="ref" href="yellow11.html#T5" target="_self" onmouseover="rs('yellow11/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E3:13_2_2_1_15"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_2_1_15"><span class="lab"><font color="Green" title="E25">A95</font></span></a>, <a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_2_1_15"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_16"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_16"/><span class="lab"><font color="Green" title="E25">A96</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_16"/><span class="lab"><font color="Green" title="E26">A97</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_2_1_16"/>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2"><span class="lab"><font color="Green" title="E12">A59</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_2_1_16"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_2_1_16"><span class="lab"><font color="Green" title="E26">A97</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E5:13_2_2_1_16"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E6:13_2_2_1_16"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T5" target="_self" onmouseover="rs('yellow11/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E7:13_2_2_1_16"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_2_1_16"><span class="lab"><font color="Green" title="E25">A96</font></span></a>, <a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E8:13_2_2_1_16"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_17"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_17"/><span class="lab"><font color="Green" title="E25">A98</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_17"/>
<font color="Maroon" title="c4">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="ref" href="yellow11.html#T5" target="_self" onmouseover="rs('yellow11/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E3:13_2_2_1_17"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_2_1_17"><span class="lab"><font color="Green" title="E25">A98</font></span></a>, <a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_2_1_17"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_18"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_18"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_18"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_2_1_18"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:13_2"><span class="lab"><font color="Green" title="E20">A67</font></span></a>, <a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_19"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_19"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_19"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><a NAME="E3:13_2_2_1_19"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_5.html#T1" onmouseover="rs('yellow_5/T1')" onmouseout="rh()">YELLOW_5:1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_2_1_19"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_20"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_20"/><span class="lab"><font color="Green" title="E25">A99</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_20"/>
<font color="Maroon" title="c6">d</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_2"><span class="lab"><font color="Green" title="E15">A62</font></span></a>, <a class="ref" href="yellow11.html#T5" target="_self" onmouseover="rs('yellow11/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E3:13_2_2_1_20"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_2_1_20"><span class="lab"><font color="Green" title="E25">A99</font></span></a>, <a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_2_1_20"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_21"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_21"/><span class="lab"><font color="Green" title="E25">A100</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_21"/><span class="lab"><font color="Green" title="E26">A101</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2"><span class="lab"><font color="Green" title="E14">A61</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_2_1_21"/>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13_2"><span class="lab"><font color="Green" title="E13">A60</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_2_1_21"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_2_1_21"><span class="lab"><font color="Green" title="E26">A101</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E5:13_2_2_1_21"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E6:13_2_2_1_21"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T5" target="_self" onmouseover="rs('yellow11/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E7:13_2_2_1_21"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_2_1_21"><span class="lab"><font color="Green" title="E25">A100</font></span></a>, <a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E8:13_2_2_1_21"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_22"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_22"/><span class="lab"><font color="Green" title="E25">A102</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_22"/><span class="lab"><font color="Green" title="E26">A103</font></span>: 
<font color="Maroon" title="c6">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_2"><span class="lab"><font color="Green" title="E15">A62</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_2_1_22"/>
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_2_1_22"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_2_1_22"><span class="lab"><font color="Green" title="E26">A103</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E5:13_2_2_1_22"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E6:13_2_2_1_22"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T5" target="_self" onmouseover="rs('yellow11/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E7:13_2_2_1_22"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_2_1_22"><span class="lab"><font color="Green" title="E25">A102</font></span></a>, <a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E8:13_2_2_1_22"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_23"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_23"/><span class="lab"><font color="Green" title="E25">A104</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_23"/>
<font color="Maroon" title="c5">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2"><span class="lab"><font color="Green" title="E14">A61</font></span></a>, <a class="ref" href="yellow11.html#T5" target="_self" onmouseover="rs('yellow11/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E3:13_2_2_1_23"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_2_1_23"><span class="lab"><font color="Green" title="E25">A104</font></span></a>, <a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_2_1_23"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_24"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_24"/><span class="lab"><font color="Green" title="E25">A105</font></span>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_24"/>
<font color="Maroon" title="c6">d</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_2"><span class="lab"><font color="Green" title="E15">A62</font></span></a>, <a class="ref" href="yellow11.html#T5" target="_self" onmouseover="rs('yellow11/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E3:13_2_2_1_24"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_2_1_24"><span class="lab"><font color="Green" title="E25">A105</font></span></a>, <a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_2_1_24"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_2_1_25"><span class="kw">suppose </span></a><a NAME="E1:13_2_2_1_25"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span></span><br/><div class="add"><a NAME="E2:13_2_2_1_25"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/><a NAME="E3:13_2_2_1_25"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_5.html#T1" onmouseover="rs('yellow_5/T1')" onmouseout="rh()">YELLOW_5:1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_2_1_25"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">K</font> =  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font> as   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>  <a href="lattice5.html#NM2" title="LATTICE5:NM.2">Sublattice</a> of <font color="Maroon" title="c2">L</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:13_2"><span class="lab"><font color="Green" title="E22">A69</font></span></a>, <a class="ref" href="yellow_0.html#D15" onmouseover="rs('yellow_0/D15')" onmouseout="rh()">YELLOW_0:def 15</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c11">K</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> ,<font color="Maroon" title="c11">K</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a> </span><br/>

<span class="kw">thus </span><a NAME="E17:13_2"/>
 <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> ,<font color="Maroon" title="c11">K</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a> 
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c12">t</font> = 3 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">td</font> = 3 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 2 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">dw</font> = 2 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E23">A106</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2_3_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c14">dw</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_2_3_1"/><span class="lab"><font color="Green" title="E24">A107</font></span>: 
<font color="Maroon" title="c14">dw</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_2_3_1"/>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c13">td</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_1"><span class="lab"><font color="Green" title="E24">A107</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E24">A108</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2_3_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c13">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_2_3_2"/><span class="lab"><font color="Green" title="E25">A109</font></span>: 
<font color="Maroon" title="c13">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_2_3_2"/>
 not 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c13">td</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_2"><span class="lab"><font color="Green" title="E25">A109</font></span></a>, <a class="ref" href="card_1.html#T51" onmouseover="rs('card_1/T51')" onmouseout="rh()">CARD_1:51</a>, <a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">reconsider </span><font color="Maroon" title="c15">tj</font> = 3 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 1 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c16">z</font> =  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/>
<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ] <span class="kw">means </span> for <font color="Olive" title="b1">X</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a>  st <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 holds <br/>( ( <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) &amp; ( <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) &amp; ( <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) &amp; ( <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) &amp; ( <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) );<br/>
<div><span class="lab"><font color="Green" title="E25">A110</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2_3_3"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c15">tj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_2_3_3"/><span class="lab"><font color="Green" title="E26">A111</font></span>: 
<font color="Maroon" title="c15">tj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_2_3_3"/>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c15">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_3"><span class="lab"><font color="Green" title="E26">A111</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E26">A112</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2_3_4"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c15">tj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_2_3_4"/><span class="lab"><font color="Green" title="E27">A113</font></span>: 
<font color="Maroon" title="c15">tj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_2_3_4"/>
 not  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c15">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_4"><span class="lab"><font color="Green" title="E27">A113</font></span></a>, <a class="ref" href="card_1.html#T51" onmouseover="rs('card_1/T51')" onmouseout="rh()">CARD_1:51</a>, <a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E27">A114</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2_3_5"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c15">tj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_2_3_5"/><span class="lab"><font color="Green" title="E28">A115</font></span>: 
<font color="Maroon" title="c15">tj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_2_3_5"/>
 not 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c13">td</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_5"><span class="lab"><font color="Green" title="E28">A115</font></span></a>, <a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E11:13_2_3"/><span class="lab"><font color="Green" title="E28">A116</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> holds <br/> ex <font color="Olive" title="b2">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>] )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2_3_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c17">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> implies  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">x</font>,<font color="Olive" title="b1">y</font>] ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:13_2_3_6"/><span class="lab"><font color="Green" title="E29">A117</font></span>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">x</font>,<font color="Olive" title="b1">y</font>] )</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_6_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:13_2_3_6_1"/>
( <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 1 or <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 2 or <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E1:13_2_3_6"><span class="lab"><font color="Green" title="E29">A117</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_6_1_1"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_6_1_1"/><span class="lab"><font color="Green" title="E30">A118</font></span>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">x</font>,<font color="Olive" title="b1">y</font>] )</span><br/><div class="add"><span class="kw">take </span><font color="Maroon" title="c18">y</font> = <font color="Maroon" title="c3">a</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c18">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c18">y</font>] )</span><br/><span class="kw">thus </span><a NAME="E2:13_2_3_6_1_1"/>
<font color="Maroon" title="c18">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">ck</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c18">y</font>]</span><br/><span class="kw">let </span><font color="Maroon" title="c19">X</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> implies ( ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) ) )</span><br/><span class="kw">thus </span><a NAME="E3:13_2_3_6_1_1"/>
( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> implies ( ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_6_1_1"><span class="lab"><font color="Green" title="E30">A118</font></span></a>, <a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_6_1_2"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_6_1_2"/><span class="lab"><font color="Green" title="E30">A119</font></span>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 1
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">x</font>,<font color="Olive" title="b1">y</font>] )</span><br/><div class="add"><span class="kw">take </span><font color="Maroon" title="c18">y</font> = <font color="Maroon" title="c6">d</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c18">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c18">y</font>] )</span><br/><span class="kw">thus </span><a NAME="E2:13_2_3_6_1_2"/>
<font color="Maroon" title="c18">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">ck</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c18">y</font>]</span><br/><span class="kw">let </span><font color="Maroon" title="c19">X</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> implies ( ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) ) )</span><br/><span class="kw">thus </span><a NAME="E3:13_2_3_6_1_2"/>
( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> implies ( ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2_3"><span class="lab"><font color="Green" title="E25">A110</font></span></a>, <a class="txt" href="#E10:13_2_3"><span class="lab"><font color="Green" title="E27">A114</font></span></a>, <a class="txt" href="#E9:13_2_3"><span class="lab"><font color="Green" title="E26">A112</font></span></a>, <a class="txt" href="#E1:13_2_3_6_1_2"><span class="lab"><font color="Green" title="E30">A119</font></span></a>, <a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_6_1_3"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_6_1_3"/><span class="lab"><font color="Green" title="E30">A120</font></span>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">x</font>,<font color="Olive" title="b1">y</font>] )</span><br/><div class="add"><span class="kw">take </span><font color="Maroon" title="c18">y</font> = <font color="Maroon" title="c5">c</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c18">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c18">y</font>] )</span><br/><span class="kw">thus </span><a NAME="E2:13_2_3_6_1_3"/>
<font color="Maroon" title="c18">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">ck</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c18">y</font>]</span><br/><span class="kw">let </span><font color="Maroon" title="c19">X</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> implies ( ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) ) )</span><br/><span class="kw">thus </span><a NAME="E3:13_2_3_6_1_3"/>
( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> implies ( ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2_3"><span class="lab"><font color="Green" title="E25">A110</font></span></a>, <a class="txt" href="#E4:13_2_3"><span class="lab"><font color="Green" title="E23">A106</font></span></a>, <a class="txt" href="#E1:13_2_3_6_1_3"><span class="lab"><font color="Green" title="E30">A120</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_6_1_4"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_6_1_4"/><span class="lab"><font color="Green" title="E30">A121</font></span>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 2
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">x</font>,<font color="Olive" title="b1">y</font>] )</span><br/><div class="add"><span class="kw">take </span><font color="Maroon" title="c18">y</font> = <font color="Maroon" title="c4">b</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c18">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c18">y</font>] )</span><br/><span class="kw">thus </span><a NAME="E2:13_2_3_6_1_4"/>
<font color="Maroon" title="c18">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">ck</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c18">y</font>]</span><br/><span class="kw">let </span><font color="Maroon" title="c19">X</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> implies ( ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) ) )</span><br/><span class="kw">thus </span><a NAME="E3:13_2_3_6_1_4"/>
( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> implies ( ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_2_3"><span class="lab"><font color="Green" title="E27">A114</font></span></a>, <a class="txt" href="#E4:13_2_3"><span class="lab"><font color="Green" title="E23">A106</font></span></a>, <a class="txt" href="#E5:13_2_3"><span class="lab"><font color="Green" title="E24">A108</font></span></a>, <a class="txt" href="#E1:13_2_3_6_1_4"><span class="lab"><font color="Green" title="E30">A121</font></span></a>, <a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_6_1_5"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_6_1_5"/><span class="lab"><font color="Green" title="E30">A122</font></span>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">x</font>,<font color="Olive" title="b1">y</font>] )</span><br/><div class="add"><span class="kw">take </span><font color="Maroon" title="c18">y</font> = <font color="Maroon" title="c7">e</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c18">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c18">y</font>] )</span><br/><span class="kw">thus </span><a NAME="E2:13_2_3_6_1_5"/>
<font color="Maroon" title="c18">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">ck</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c18">y</font>]</span><br/><span class="kw">let </span><font color="Maroon" title="c19">X</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> implies ( ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) ) )</span><br/><span class="kw">thus </span><a NAME="E3:13_2_3_6_1_5"/>
( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> implies ( ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13_2_3"><span class="lab"><font color="Green" title="E26">A112</font></span></a>, <a class="txt" href="#E5:13_2_3"><span class="lab"><font color="Green" title="E24">A108</font></span></a>, <a class="txt" href="#E1:13_2_3_6_1_5"><span class="lab"><font color="Green" title="E30">A122</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="kw">consider </span><font color="Maroon" title="c17">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a>,<font color="Maroon" title="c9">ck</font><span class="kw"> such that </span><br/><a NAME="E13:13_2_3"/><span class="lab"><font color="Green" title="E29">A123</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c17">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>]
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S1" onmouseover="rs('funct_2/S1')" onmouseout="rh()">FUNCT_2:sch 1</a>(<a class="txt" href="#E11:13_2_3"><span class="lab"><font color="Green" title="E28">A116</font></span></a>);<br/></span>
<span class="kw">reconsider </span><font color="Maroon" title="c18">f</font> = <font color="Maroon" title="c17">f</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a>,<font color="Maroon" title="c11">K</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a></span>;<br/>
<div><span class="lab"><font color="Green" title="E30">A124</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2_3_7"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a>  st <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">y</font> holds <br/><font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">x</font>, <font color="Maroon" title="c20">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> implies <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font> )</span><br/><span class="kw">assume </span><a NAME="E1:13_2_3_7"/><span class="lab"><font color="Green" title="E31">A125</font></span>: 
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><span class="kw">thus </span><a NAME="E2:13_2_3_7"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2_3_7_1"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:13_2_3_7_1_1"/>
( ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_1"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_2_3_7_1_1_1"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_2"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_2_3_7_1_1_2"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_3"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_2_3_7_1_1_3"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_4"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_4"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_2_3_7_1_1_4"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_5"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_5"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_2_3_7_1_1_5"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_6"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_6"/><span class="lab"><font color="Green" title="E32">A126</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_6"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_6"><span class="lab"><font color="Green" title="E32">A126</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_7"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_7"/><span class="lab"><font color="Green" title="E32">A127</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_7"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_7"><span class="lab"><font color="Green" title="E32">A127</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_8"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_8"/><span class="lab"><font color="Green" title="E32">A128</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_8"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_8"><span class="lab"><font color="Green" title="E32">A128</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_9"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_9"/><span class="lab"><font color="Green" title="E32">A129</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_9"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_9"><span class="lab"><font color="Green" title="E32">A129</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_10"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_10"/><span class="lab"><font color="Green" title="E32">A130</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_10"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_10"><span class="lab"><font color="Green" title="E32">A130</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_11"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_11"/><span class="lab"><font color="Green" title="E32">A131</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_11"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_11"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_11"><span class="lab"><font color="Green" title="E32">A131</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_12"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_12"/><span class="lab"><font color="Green" title="E32">A132</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_12"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_12"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_12"><span class="lab"><font color="Green" title="E32">A132</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_13"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_13"/><span class="lab"><font color="Green" title="E32">A133</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_13"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_13"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_13"><span class="lab"><font color="Green" title="E32">A133</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_14"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_14"/><span class="lab"><font color="Green" title="E32">A134</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_14"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_14"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_14"><span class="lab"><font color="Green" title="E32">A134</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_15"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_15"/><span class="lab"><font color="Green" title="E32">A135</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_15"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_15"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_15"><span class="lab"><font color="Green" title="E32">A135</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_16"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_16"/><span class="lab"><font color="Green" title="E32">A136</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_16"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_16"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_16"><span class="lab"><font color="Green" title="E32">A136</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_17"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_17"/><span class="lab"><font color="Green" title="E32">A137</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_17"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_17"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_17"><span class="lab"><font color="Green" title="E32">A137</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_18"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_18"/><span class="lab"><font color="Green" title="E32">A138</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_18"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_18"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_18"><span class="lab"><font color="Green" title="E32">A138</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_19"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_19"/><span class="lab"><font color="Green" title="E32">A139</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_19"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_19"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_19"><span class="lab"><font color="Green" title="E32">A139</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_20"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_20"/><span class="lab"><font color="Green" title="E32">A140</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_20"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_20"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_20"><span class="lab"><font color="Green" title="E32">A140</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_21"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_21"/><span class="lab"><font color="Green" title="E32">A141</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_21"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_21"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_21"><span class="lab"><font color="Green" title="E32">A141</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_22"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_22"/><span class="lab"><font color="Green" title="E32">A142</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_22"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_22"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_22"><span class="lab"><font color="Green" title="E32">A142</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_23"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_23"/><span class="lab"><font color="Green" title="E32">A143</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_23"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_23"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_23"><span class="lab"><font color="Green" title="E32">A143</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_24"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_24"/><span class="lab"><font color="Green" title="E32">A144</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_24"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_24"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_24"><span class="lab"><font color="Green" title="E32">A144</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_7_1_1_25"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_7_1_1_25"/><span class="lab"><font color="Green" title="E32">A145</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_7_1_1_25"/><span class="kw">then </span>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_7_1_1_25"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_7"><span class="lab"><font color="Green" title="E31">A125</font></span></a>, <a class="txt" href="#E1:13_2_3_7_1_1_25"><span class="lab"><font color="Green" title="E32">A145</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<a NAME="E16:13_2_3"/><span class="lab"><font color="Green" title="E31">A146</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c18">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">ck</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2_3_8"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c19">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c18">f</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:13_2_3_8"/>
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c18">f</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c20">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:13_2_3_8"/><span class="lab"><font color="Green" title="E32">A147</font></span>: 
<font color="Maroon" title="c20">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c18">f</font>
 <span class="kw">and </span><br/><a NAME="E4:13_2_3_8"/><span class="lab"><font color="Green" title="E33">A148</font></span>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c21">x</font> = <font color="Maroon" title="c20">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_3_8"><span class="lab"><font color="Green" title="E32">A147</font></span></a></span>;<br/>
<a NAME="E6:13_2_3_8"/>
( <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> or <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> or <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> or <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> or <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/>
<a NAME="E7:13_2_3_8"/><span class="kw">then </span>
( <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E4:13_2_3_8"><span class="lab"><font color="Green" title="E33">A148</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:13_2_3_8"/>
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E17:13_2_3"/><span class="lab"><font color="Green" title="E32">A149</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c18">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E18:13_2_3"/>
<font color="Maroon" title="c9">ck</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c18">f</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2_3_9"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c19">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c18">f</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:13_2_3_9"/><span class="lab"><font color="Green" title="E33">A150</font></span>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c18">f</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_9_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:13_2_3_9_1"/>
( <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_9"><span class="lab"><font color="Green" title="E33">A150</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_9_1_1"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_9_1_1"/><span class="lab"><font color="Green" title="E34">A151</font></span>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c18">f</font></span><br/><div class="add"><a NAME="E2:13_2_3_9_1_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_9_1_1"/>
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c18">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:13_2_3"><span class="lab"><font color="Green" title="E32">A149</font></span></a>, <a class="txt" href="#E1:13_2_3_9_1_1"><span class="lab"><font color="Green" title="E34">A151</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_9_1_2"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_9_1_2"/><span class="lab"><font color="Green" title="E34">A152</font></span>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c18">f</font></span><br/><div class="add"><a NAME="E2:13_2_3_9_1_2"/>
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">td</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_9_1_2"/>
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c18">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:13_2_3"><span class="lab"><font color="Green" title="E32">A149</font></span></a>, <a class="txt" href="#E1:13_2_3_9_1_2"><span class="lab"><font color="Green" title="E34">A152</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_9_1_3"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_9_1_3"/><span class="lab"><font color="Green" title="E34">A153</font></span>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c18">f</font></span><br/><div class="add"><a NAME="E2:13_2_3_9_1_3"/>
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c14">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_9_1_3"/>
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c18">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:13_2_3"><span class="lab"><font color="Green" title="E32">A149</font></span></a>, <a class="txt" href="#E1:13_2_3_9_1_3"><span class="lab"><font color="Green" title="E34">A153</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_9_1_4"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_9_1_4"/><span class="lab"><font color="Green" title="E34">A154</font></span>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c18">f</font></span><br/><div class="add"><a NAME="E2:13_2_3_9_1_4"/>
<font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_9_1_4"/>
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c18">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:13_2_3"><span class="lab"><font color="Green" title="E32">A149</font></span></a>, <a class="txt" href="#E1:13_2_3_9_1_4"><span class="lab"><font color="Green" title="E34">A154</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_9_1_5"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_9_1_5"/><span class="lab"><font color="Green" title="E34">A155</font></span>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c18">f</font></span><br/><div class="add"><a NAME="E2:13_2_3_9_1_5"/>
<font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_9_1_5"/>
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c18">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:13_2_3"><span class="lab"><font color="Green" title="E32">A149</font></span></a>, <a class="txt" href="#E1:13_2_3_9_1_5"><span class="lab"><font color="Green" title="E34">A155</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<a NAME="E19:13_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A156</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c18">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">ck</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:13_2_3"><span class="lab"><font color="Green" title="E31">A146</font></span></a></span>;<br/>
<a NAME="E20:13_2_3"/><span class="lab"><font color="Green" title="E34">A157</font></span>: 
 for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a> holds <br/> ( <font color="Olive" title="b1">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b2">y</font> iff <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">y</font> )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2_3_10"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c19">x</font>, <font color="Maroon" title="c20">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K1" title="YELLOW11:func.1">N_5</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font> iff <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> )</span><br/>

<span class="kw">thus </span><a NAME="E1:13_2_3_10"/>
( <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font> implies <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> )
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> implies <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font> )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2_3_10_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_2_3_10_1"/><span class="lab"><font color="Green" title="E35">A158</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:13_2_3_10_1_1"/>
( ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_1"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_2_3_10_1_1_1"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_2"/><span class="lab"><font color="Green" title="E36">A159</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A160</font></span>: 
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><a NAME="E3:13_2_3_10_1_1_2"/><span class="lab"><font color="Green" title="E38">A161</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2"><span class="lab"><font color="Green" title="E12">A59</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_3_10_1_1_2"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_2"><span class="lab"><font color="Green" title="E36">A159</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:13_2_3_10_1_1_2"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_3_10_1_1_2"><span class="lab"><font color="Green" title="E37">A160</font></span></a>, <a class="txt" href="#E3:13_2_3_10_1_1_2"><span class="lab"><font color="Green" title="E38">A161</font></span></a>, <a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_3"/><span class="lab"><font color="Green" title="E36">A162</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A163</font></span>: 
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><a NAME="E3:13_2_3_10_1_1_3"/><span class="lab"><font color="Green" title="E38">A164</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13_2"><span class="lab"><font color="Green" title="E13">A60</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_3_10_1_1_3"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_3"><span class="lab"><font color="Green" title="E36">A162</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:13_2_3_10_1_1_3"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_3_10_1_1_3"><span class="lab"><font color="Green" title="E37">A163</font></span></a>, <a class="txt" href="#E3:13_2_3_10_1_1_3"><span class="lab"><font color="Green" title="E38">A164</font></span></a>, <a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_4"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_4"/><span class="lab"><font color="Green" title="E36">A165</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_4"/><span class="lab"><font color="Green" title="E37">A166</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_3_10_1_1_4"/>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2"><span class="lab"><font color="Green" title="E12">A59</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_3_10_1_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A167</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_3_10_1_1_4"><span class="lab"><font color="Green" title="E37">A166</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E5:13_2_3_10_1_1_4"/><span class="lab"><font color="Green" title="E39">A168</font></span>: 
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_4"><span class="lab"><font color="Green" title="E36">A165</font></span></a></span>;<br/><a NAME="E6:13_2_3_10_1_1_4"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_4"><span class="lab"><font color="Green" title="E36">A165</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E7:13_2_3_10_1_1_4"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2_3_10_1_1_4"><span class="lab"><font color="Green" title="E39">A168</font></span></a>, <a class="txt" href="#E4:13_2_3_10_1_1_4"><span class="lab"><font color="Green" title="E38">A167</font></span></a>, <a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_5"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_5"/><span class="lab"><font color="Green" title="E36">A169</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_5"/><span class="lab"><font color="Green" title="E37">A170</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2"><span class="lab"><font color="Green" title="E14">A61</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_3_10_1_1_5"/>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13_2"><span class="lab"><font color="Green" title="E13">A60</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_3_10_1_1_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A171</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_3_10_1_1_5"><span class="lab"><font color="Green" title="E37">A170</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E5:13_2_3_10_1_1_5"/><span class="lab"><font color="Green" title="E39">A172</font></span>: 
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_5"><span class="lab"><font color="Green" title="E36">A169</font></span></a></span>;<br/><a NAME="E6:13_2_3_10_1_1_5"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_5"><span class="lab"><font color="Green" title="E36">A169</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E7:13_2_3_10_1_1_5"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2_3_10_1_1_5"><span class="lab"><font color="Green" title="E39">A172</font></span></a>, <a class="txt" href="#E4:13_2_3_10_1_1_5"><span class="lab"><font color="Green" title="E38">A171</font></span></a>, <a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_6"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_6"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c13">td</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c16">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_10_1"><span class="lab"><font color="Green" title="E35">A158</font></span></a>, <a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_10_1_1_6"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_7"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_7"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_2_3_10_1_1_7"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_8"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_8"/><span class="lab"><font color="Green" title="E36">A173</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_8"/><span class="lab"><font color="Green" title="E37">A174</font></span>: 
 not 2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c14">dw</font>
 ;<br/><a NAME="E3:13_2_3_10_1_1_8"/>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c13">td</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><a NAME="E4:13_2_3_10_1_1_8"/><span class="kw">then </span>
 not <font color="Maroon" title="c13">td</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c14">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_3_10_1_1_8"><span class="lab"><font color="Green" title="E37">A174</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:13_2_3_10_1_1_8"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_10_1"><span class="lab"><font color="Green" title="E35">A158</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_8"><span class="lab"><font color="Green" title="E36">A173</font></span></a>, <a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_9"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_9"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c13">td</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c16">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_10_1"><span class="lab"><font color="Green" title="E35">A158</font></span></a>, <a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_10_1_1_9"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_10"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_10"/><span class="lab"><font color="Green" title="E36">A175</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A176</font></span>: 
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><a NAME="E3:13_2_3_10_1_1_10"/><span class="lab"><font color="Green" title="E38">A177</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_3_10_1_1_10"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_10"><span class="lab"><font color="Green" title="E36">A175</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:13_2_3_10_1_1_10"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_3_10_1_1_10"><span class="lab"><font color="Green" title="E37">A176</font></span></a>, <a class="txt" href="#E3:13_2_3_10_1_1_10"><span class="lab"><font color="Green" title="E38">A177</font></span></a>, <a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_11"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_11"/><span class="lab"><font color="Green" title="E36">A178</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_11"/><span class="lab"><font color="Green" title="E37">A179</font></span>: 
<font color="Maroon" title="c6">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_2"><span class="lab"><font color="Green" title="E15">A62</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_3_10_1_1_11"/>
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_3_10_1_1_11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A180</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_3_10_1_1_11"><span class="lab"><font color="Green" title="E37">A179</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E5:13_2_3_10_1_1_11"/><span class="lab"><font color="Green" title="E39">A181</font></span>: 
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_11"><span class="lab"><font color="Green" title="E36">A178</font></span></a></span>;<br/><a NAME="E6:13_2_3_10_1_1_11"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_11"><span class="lab"><font color="Green" title="E36">A178</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E7:13_2_3_10_1_1_11"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2_3_10_1_1_11"><span class="lab"><font color="Green" title="E39">A181</font></span></a>, <a class="txt" href="#E4:13_2_3_10_1_1_11"><span class="lab"><font color="Green" title="E38">A180</font></span></a>, <a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_12"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_12"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_12"/><span class="kw">then </span>
<font color="Maroon" title="c14">dw</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c16">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_10_1"><span class="lab"><font color="Green" title="E35">A158</font></span></a>, <a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_10_1_1_12"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_13"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_13"/><span class="lab"><font color="Green" title="E36">A182</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_13"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c14">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T50" onmouseover="rs('card_1/T50')" onmouseout="rh()">CARD_1:50</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><a NAME="E3:13_2_3_10_1_1_13"/><span class="kw">then </span>
 not <font color="Maroon" title="c14">dw</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">td</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_3_10_1_1_13"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_10_1"><span class="lab"><font color="Green" title="E35">A158</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_13"><span class="lab"><font color="Green" title="E36">A182</font></span></a>, <a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_14"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_14"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_2_3_10_1_1_14"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_15"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_15"/><span class="lab"><font color="Green" title="E36">A183</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_15"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c14">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T50" onmouseover="rs('card_1/T50')" onmouseout="rh()">CARD_1:50</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><a NAME="E3:13_2_3_10_1_1_15"/><span class="kw">then </span>
 not <font color="Maroon" title="c14">dw</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c15">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_3_10_1_1_15"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_10_1"><span class="lab"><font color="Green" title="E35">A158</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_15"><span class="lab"><font color="Green" title="E36">A183</font></span></a>, <a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_16"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_16"/><span class="lab"><font color="Green" title="E36">A184</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_16"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A185</font></span>: 
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><a NAME="E3:13_2_3_10_1_1_16"/><span class="lab"><font color="Green" title="E38">A186</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2"><span class="lab"><font color="Green" title="E14">A61</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_3_10_1_1_16"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_16"><span class="lab"><font color="Green" title="E36">A184</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:13_2_3_10_1_1_16"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_3_10_1_1_16"><span class="lab"><font color="Green" title="E37">A185</font></span></a>, <a class="txt" href="#E3:13_2_3_10_1_1_16"><span class="lab"><font color="Green" title="E38">A186</font></span></a>, <a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_17"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_17"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_17"/><span class="kw">then </span>
<font color="Maroon" title="c15">tj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c16">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_10_1"><span class="lab"><font color="Green" title="E35">A158</font></span></a>, <a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_10_1_1_17"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_18"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_18"/><span class="lab"><font color="Green" title="E36">A187</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_18"/>
1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c15">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><a NAME="E3:13_2_3_10_1_1_18"/><span class="kw">then </span>
 not <font color="Maroon" title="c15">tj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">td</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_3_10_1_1_18"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_10_1"><span class="lab"><font color="Green" title="E35">A158</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_18"><span class="lab"><font color="Green" title="E36">A187</font></span></a>, <a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_19"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_19"/><span class="lab"><font color="Green" title="E36">A188</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_19"/><span class="lab"><font color="Green" title="E37">A189</font></span>: 
 not 2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c14">dw</font>
 ;<br/><a NAME="E3:13_2_3_10_1_1_19"/>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c15">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><a NAME="E4:13_2_3_10_1_1_19"/><span class="kw">then </span>
 not <font color="Maroon" title="c15">tj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c14">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_3_10_1_1_19"><span class="lab"><font color="Green" title="E37">A189</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:13_2_3_10_1_1_19"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_10_1"><span class="lab"><font color="Green" title="E35">A158</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_19"><span class="lab"><font color="Green" title="E36">A188</font></span></a>, <a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_20"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_20"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_2_3_10_1_1_20"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_21"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_21"/><span class="lab"><font color="Green" title="E36">A190</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A191</font></span>: 
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><a NAME="E3:13_2_3_10_1_1_21"/><span class="lab"><font color="Green" title="E38">A192</font></span>: 
<font color="Maroon" title="c6">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_2"><span class="lab"><font color="Green" title="E15">A62</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_3_10_1_1_21"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_21"><span class="lab"><font color="Green" title="E36">A190</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:13_2_3_10_1_1_21"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_3_10_1_1_21"><span class="lab"><font color="Green" title="E37">A191</font></span></a>, <a class="txt" href="#E3:13_2_3_10_1_1_21"><span class="lab"><font color="Green" title="E38">A192</font></span></a>, <a class="ref" href="yellow_0.html#T60" onmouseover="rs('yellow_0/T60')" onmouseout="rh()">YELLOW_0:60</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_22"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_22"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">z</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_22"/><span class="kw">then </span>
<font color="Maroon" title="c12">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c16">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_10_1"><span class="lab"><font color="Green" title="E35">A158</font></span></a>, <a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_10_1_1_22"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_23"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_23"/><span class="lab"><font color="Green" title="E36">A193</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_23"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c12">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T51" onmouseover="rs('card_1/T51')" onmouseout="rh()">CARD_1:51</a>, <a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</a></span>;<br/><a NAME="E3:13_2_3_10_1_1_23"/><span class="kw">then </span>
 not <font color="Maroon" title="c12">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">td</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T4" target="_self" onmouseover="rs('yellow11/T4')" onmouseout="rh()">Th4</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_3_10_1_1_23"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_10_1"><span class="lab"><font color="Green" title="E35">A158</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_23"><span class="lab"><font color="Green" title="E36">A193</font></span></a>, <a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_24"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_24"/><span class="lab"><font color="Green" title="E36">A194</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dw</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_24"/><span class="lab"><font color="Green" title="E37">A195</font></span>: 
 not 2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c14">dw</font>
 ;<br/><a NAME="E3:13_2_3_10_1_1_24"/>
2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c12">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T51" onmouseover="rs('card_1/T51')" onmouseout="rh()">CARD_1:51</a>, <a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</a></span>;<br/><a NAME="E4:13_2_3_10_1_1_24"/><span class="kw">then </span>
 not <font color="Maroon" title="c12">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c14">dw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_3_10_1_1_24"><span class="lab"><font color="Green" title="E37">A195</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:13_2_3_10_1_1_24"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_10_1"><span class="lab"><font color="Green" title="E35">A158</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_24"><span class="lab"><font color="Green" title="E36">A194</font></span></a>, <a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_25"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_25"/><span class="lab"><font color="Green" title="E36">A196</font></span>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_1_1_25"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c12">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T51" onmouseover="rs('card_1/T51')" onmouseout="rh()">CARD_1:51</a>, <a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</a></span>;<br/><a NAME="E3:13_2_3_10_1_1_25"/><span class="kw">then </span>
 not <font color="Maroon" title="c12">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c15">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#T3" target="_self" onmouseover="rs('yellow11/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_3_10_1_1_25"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_3_10_1"><span class="lab"><font color="Green" title="E35">A158</font></span></a>, <a class="txt" href="#E1:13_2_3_10_1_1_25"><span class="lab"><font color="Green" title="E36">A196</font></span></a>, <a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_1_1_26"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_1_1_26"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">t</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_2_3_10_1_1_26"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E2:13_2_3_10"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> implies <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font> )
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2_3_10_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:13_2_3_10_2"/><span class="lab"><font color="Green" title="E35">A197</font></span>: 
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">ck</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:13_2_3"><span class="lab"><font color="Green" title="E32">A149</font></span></a>, <a class="txt" href="#E19:13_2_3"><span class="lab"><font color="Green" title="E33">A156</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<a NAME="E2:13_2_3_10_2"/><span class="lab"><font color="Green" title="E36">A198</font></span>: 
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">ck</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:13_2_3"><span class="lab"><font color="Green" title="E32">A149</font></span></a>, <a class="txt" href="#E19:13_2_3"><span class="lab"><font color="Green" title="E33">A156</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:13_2_3_10_2"/><span class="lab"><font color="Green" title="E37">A199</font></span>: 
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:13_2_3_10_2_1"/>
( ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_3_10_2"><span class="lab"><font color="Green" title="E36">A198</font></span></a>, <a class="txt" href="#E1:13_2_3_10_2"><span class="lab"><font color="Green" title="E35">A197</font></span></a>, <a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_1"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_2_3_10_2_1_1"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_2"/><span class="lab"><font color="Green" title="E38">A200</font></span>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_2"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><a NAME="E3:13_2_3_10_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c16">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a>, <a class="txt" href="#E1:13_2_3_10_2_1_2"><span class="lab"><font color="Green" title="E38">A200</font></span></a></span>;<br/><a NAME="E4:13_2_3_10_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c19">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c20">y</font>
 ;<br/><span class="kw">hence </span><a NAME="E5:13_2_3_10_2_1_2"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_3"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_3"/><span class="lab"><font color="Green" title="E38">A201</font></span>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_3"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><a NAME="E3:13_2_3_10_2_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c16">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a>, <a class="txt" href="#E1:13_2_3_10_2_1_3"><span class="lab"><font color="Green" title="E38">A201</font></span></a></span>;<br/><a NAME="E4:13_2_3_10_2_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c19">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c20">y</font>
 ;<br/><span class="kw">hence </span><a NAME="E5:13_2_3_10_2_1_3"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_4"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_4"/><span class="lab"><font color="Green" title="E38">A202</font></span>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_4"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><a NAME="E3:13_2_3_10_2_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c16">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a>, <a class="txt" href="#E1:13_2_3_10_2_1_4"><span class="lab"><font color="Green" title="E38">A202</font></span></a></span>;<br/><a NAME="E4:13_2_3_10_2_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c19">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c20">y</font>
 ;<br/><span class="kw">hence </span><a NAME="E5:13_2_3_10_2_1_4"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_5"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_5"/><span class="lab"><font color="Green" title="E38">A203</font></span>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_5"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><a NAME="E3:13_2_3_10_2_1_5"/><span class="kw">then </span>
<font color="Maroon" title="c16">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a>, <a class="txt" href="#E1:13_2_3_10_2_1_5"><span class="lab"><font color="Green" title="E38">A203</font></span></a></span>;<br/><a NAME="E4:13_2_3_10_2_1_5"/><span class="kw">then </span>
<font color="Maroon" title="c19">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c20">y</font>
 ;<br/><span class="kw">hence </span><a NAME="E5:13_2_3_10_2_1_5"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_6"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_6"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_3_10_2"><span class="lab"><font color="Green" title="E37">A199</font></span></a>, <a class="ref" href="yellow_0.html#T59" onmouseover="rs('yellow_0/T59')" onmouseout="rh()">YELLOW_0:59</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_10_2_1_6"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E3:13_2"><span class="lab"><font color="Green" title="E12">A59</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_7"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_7"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_2_3_10_2_1_7"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_8"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_8"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_3_10_2"><span class="lab"><font color="Green" title="E37">A199</font></span></a>, <a class="ref" href="yellow_0.html#T59" onmouseover="rs('yellow_0/T59')" onmouseout="rh()">YELLOW_0:59</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_10_2_1_8"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E7:13_2"><span class="lab"><font color="Green" title="E16">A63</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_9"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_9"/><span class="lab"><font color="Green" title="E38">A204</font></span>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_9"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">tj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><a NAME="E3:13_2_3_10_2_1_9"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A205</font></span>: 
<font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">tj</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a>, <a class="txt" href="#E1:13_2_3_10_2_1_9"><span class="lab"><font color="Green" title="E38">A204</font></span></a></span>;<br/><a NAME="E4:13_2_3_10_2_1_9"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><a NAME="E5:13_2_3_10_2_1_9"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A206</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">td</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a>, <a class="txt" href="#E1:13_2_3_10_2_1_9"><span class="lab"><font color="Green" title="E38">A204</font></span></a></span>;<br/><a NAME="E6:13_2_3_10_2_1_9"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> 1 <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> 2
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T39" onmouseover="rs('nat_1/T39')" onmouseout="rh()">NAT_1:39</a></span>;<br/><a NAME="E7:13_2_3_10_2_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c19">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2_3_10_2_1_9"><span class="lab"><font color="Green" title="E40">A206</font></span></a>, <a class="txt" href="#E3:13_2_3_10_2_1_9"><span class="lab"><font color="Green" title="E39">A205</font></span></a>, <a class="ref" href="xboole_1.html#T34" onmouseover="rs('xboole_1/T34')" onmouseout="rh()">XBOOLE_1:34</a></span>;<br/><span class="kw">hence </span><a NAME="E8:13_2_3_10_2_1_9"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_10"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_10"/><span class="lab"><font color="Green" title="E38">A207</font></span>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_10"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><a NAME="E3:13_2_3_10_2_1_10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A208</font></span>: 
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a>, <a class="txt" href="#E1:13_2_3_10_2_1_10"><span class="lab"><font color="Green" title="E38">A207</font></span></a></span>;<br/><a NAME="E4:13_2_3_10_2_1_10"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><a NAME="E5:13_2_3_10_2_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c13">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a>, <a class="txt" href="#E1:13_2_3_10_2_1_10"><span class="lab"><font color="Green" title="E38">A207</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E6:13_2_3_10_2_1_10"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_3_10_2_1_10"><span class="lab"><font color="Green" title="E39">A208</font></span></a>, <a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_11"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_11"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_11"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_3_10_2"><span class="lab"><font color="Green" title="E37">A199</font></span></a>, <a class="ref" href="yellow_0.html#T59" onmouseover="rs('yellow_0/T59')" onmouseout="rh()">YELLOW_0:59</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_10_2_1_11"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E4:13_2"><span class="lab"><font color="Green" title="E13">A60</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_12"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_12"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_12"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_3_10_2"><span class="lab"><font color="Green" title="E37">A199</font></span></a>, <a class="ref" href="yellow_0.html#T59" onmouseover="rs('yellow_0/T59')" onmouseout="rh()">YELLOW_0:59</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_10_2_1_12"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E7:13_2"><span class="lab"><font color="Green" title="E16">A63</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_13"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_13"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_2_3_10_2_1_13"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_14"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_14"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_14"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_3_10_2"><span class="lab"><font color="Green" title="E37">A199</font></span></a>, <a class="ref" href="yellow_0.html#T59" onmouseover="rs('yellow_0/T59')" onmouseout="rh()">YELLOW_0:59</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_10_2_1_14"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E9:13_2"><span class="lab"><font color="Green" title="E18">A65</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_15"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_15"/><span class="lab"><font color="Green" title="E38">A209</font></span>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_15"/><span class="lab"><font color="Green" title="E39">A210</font></span>: 
<font color="Maroon" title="c14">dw</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">t</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="13_2_3_10_2_1_15_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c21">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c21">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">dw</font> or <font color="Maroon" title="c21">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">t</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:13_2_3_10_2_1_15_1"/>
<font color="Maroon" title="c21">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">dw</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c21">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">t</font></span><br/>

<a NAME="E2:13_2_3_10_2_1_15_1"/><span class="kw">then </span>
( <font color="Maroon" title="c21">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or <font color="Maroon" title="c21">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T50" onmouseover="rs('card_1/T50')" onmouseout="rh()">CARD_1:50</a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:13_2_3_10_2_1_15_1"/>
<font color="Maroon" title="c21">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T51" onmouseover="rs('card_1/T51')" onmouseout="rh()">CARD_1:51</a>, <a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E3:13_2_3_10_2_1_15"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><a NAME="E4:13_2_3_10_2_1_15"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A211</font></span>: 
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a>, <a class="txt" href="#E1:13_2_3_10_2_1_15"><span class="lab"><font color="Green" title="E38">A209</font></span></a></span>;<br/><a NAME="E5:13_2_3_10_2_1_15"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c14">dw</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><a NAME="E6:13_2_3_10_2_1_15"/><span class="kw">then </span>
<font color="Maroon" title="c14">dw</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a>, <a class="txt" href="#E1:13_2_3_10_2_1_15"><span class="lab"><font color="Green" title="E38">A209</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E7:13_2_3_10_2_1_15"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_3_10_2_1_15"><span class="lab"><font color="Green" title="E39">A210</font></span></a>, <a class="txt" href="#E4:13_2_3_10_2_1_15"><span class="lab"><font color="Green" title="E40">A211</font></span></a>, <a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_16"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_16"/><span class="lab"><font color="Green" title="E38">A212</font></span>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_16"/><span class="lab"><font color="Green" title="E39">A213</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2"><span class="lab"><font color="Green" title="E12">A59</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_3_10_2_1_16"/>
<font color="Maroon" title="c6">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_3_10_2"><span class="lab"><font color="Green" title="E37">A199</font></span></a>, <a class="txt" href="#E1:13_2_3_10_2_1_16"><span class="lab"><font color="Green" title="E38">A212</font></span></a>, <a class="ref" href="yellow_0.html#T59" onmouseover="rs('yellow_0/T59')" onmouseout="rh()">YELLOW_0:59</a></span>;<br/><a NAME="E4:13_2_3_10_2_1_16"/><span class="kw">then </span>
<font color="Maroon" title="c6">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_3_10_2_1_16"><span class="lab"><font color="Green" title="E39">A213</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><span class="kw">hence </span><a NAME="E5:13_2_3_10_2_1_16"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_17"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_17"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_17"/><span class="kw">then </span>
<font color="Maroon" title="c6">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_3_10_2"><span class="lab"><font color="Green" title="E37">A199</font></span></a>, <a class="ref" href="yellow_0.html#T59" onmouseover="rs('yellow_0/T59')" onmouseout="rh()">YELLOW_0:59</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_10_2_1_17"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_18"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_18"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_18"/><span class="kw">then </span>
<font color="Maroon" title="c6">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_3_10_2"><span class="lab"><font color="Green" title="E37">A199</font></span></a>, <a class="ref" href="yellow_0.html#T59" onmouseover="rs('yellow_0/T59')" onmouseout="rh()">YELLOW_0:59</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_10_2_1_18"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E9:13_2"><span class="lab"><font color="Green" title="E18">A65</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_19"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_19"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_2_3_10_2_1_19"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_20"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_20"/><span class="lab"><font color="Green" title="E38">A214</font></span>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_20"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><a NAME="E3:13_2_3_10_2_1_20"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A215</font></span>: 
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a>, <a class="txt" href="#E1:13_2_3_10_2_1_20"><span class="lab"><font color="Green" title="E38">A214</font></span></a></span>;<br/><a NAME="E4:13_2_3_10_2_1_20"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">tj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2_3"><span class="lab"><font color="Green" title="E29">A123</font></span></a></span>;<br/><a NAME="E5:13_2_3_10_2_1_20"/><span class="kw">then </span>
<font color="Maroon" title="c15">tj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a>, <a class="txt" href="#E1:13_2_3_10_2_1_20"><span class="lab"><font color="Green" title="E38">A214</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E6:13_2_3_10_2_1_20"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_3_10_2_1_20"><span class="lab"><font color="Green" title="E39">A215</font></span></a>, <a class="ref" href="yellow_1.html#T3" onmouseover="rs('yellow_1/T3')" onmouseout="rh()">YELLOW_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_21"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_21"/><span class="lab"><font color="Green" title="E38">A216</font></span>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_21"/><span class="lab"><font color="Green" title="E39">A217</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_3_10_2_1_21"/><span class="lab"><font color="Green" title="E40">A218</font></span>: 
<font color="Maroon" title="c6">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_2"><span class="lab"><font color="Green" title="E15">A62</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_3_10_2_1_21"/>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2"><span class="lab"><font color="Green" title="E12">A59</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E5:13_2_3_10_2_1_21"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_3_10_2_1_21"><span class="lab"><font color="Green" title="E39">A217</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E6:13_2_3_10_2_1_21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A219</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_3_10_2_1_21"><span class="lab"><font color="Green" title="E40">A218</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E7:13_2_3_10_2_1_21"/>
<font color="Maroon" title="c7">e</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_3_10_2"><span class="lab"><font color="Green" title="E37">A199</font></span></a>, <a class="txt" href="#E1:13_2_3_10_2_1_21"><span class="lab"><font color="Green" title="E38">A216</font></span></a>, <a class="ref" href="yellow_0.html#T59" onmouseover="rs('yellow_0/T59')" onmouseout="rh()">YELLOW_0:59</a></span>;<br/><span class="kw">hence </span><a NAME="E8:13_2_3_10_2_1_21"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E6:13_2_3_10_2_1_21"><span class="lab"><font color="Green" title="E41">A219</font></span></a>, <a class="ref" href="orders_2.html#T2" onmouseover="rs('orders_2/T2')" onmouseout="rh()">ORDERS_2:2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_22"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_22"/><span class="lab"><font color="Green" title="E38">A220</font></span>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_22"/><span class="lab"><font color="Green" title="E39">A221</font></span>: 
<font color="Maroon" title="c6">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_2"><span class="lab"><font color="Green" title="E15">A62</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E3:13_2_3_10_2_1_22"/>
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2"><span class="lab"><font color="Green" title="E17">A64</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>;<br/><a NAME="E4:13_2_3_10_2_1_22"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A222</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_3_10_2_1_22"><span class="lab"><font color="Green" title="E39">A221</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/><a NAME="E5:13_2_3_10_2_1_22"/>
<font color="Maroon" title="c7">e</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_3_10_2"><span class="lab"><font color="Green" title="E37">A199</font></span></a>, <a class="txt" href="#E1:13_2_3_10_2_1_22"><span class="lab"><font color="Green" title="E38">A220</font></span></a>, <a class="ref" href="yellow_0.html#T59" onmouseover="rs('yellow_0/T59')" onmouseout="rh()">YELLOW_0:59</a></span>;<br/><span class="kw">hence </span><a NAME="E6:13_2_3_10_2_1_22"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E4:13_2_3_10_2_1_22"><span class="lab"><font color="Green" title="E40">A222</font></span></a>, <a class="ref" href="orders_2.html#T2" onmouseover="rs('orders_2/T2')" onmouseout="rh()">ORDERS_2:2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_23"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_23"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_23"/><span class="kw">then </span>
<font color="Maroon" title="c7">e</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_3_10_2"><span class="lab"><font color="Green" title="E37">A199</font></span></a>, <a class="ref" href="yellow_0.html#T59" onmouseover="rs('yellow_0/T59')" onmouseout="rh()">YELLOW_0:59</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_10_2_1_23"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E5:13_2"><span class="lab"><font color="Green" title="E14">A61</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_24"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_24"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><a NAME="E2:13_2_3_10_2_1_24"/><span class="kw">then </span>
<font color="Maroon" title="c7">e</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_3_10_2"><span class="lab"><font color="Green" title="E37">A199</font></span></a>, <a class="ref" href="yellow_0.html#T59" onmouseover="rs('yellow_0/T59')" onmouseout="rh()">YELLOW_0:59</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_3_10_2_1_24"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E11">AAA</font></span></a>, <a class="txt" href="#E6:13_2"><span class="lab"><font color="Green" title="E15">A62</font></span></a>, <a class="ref" href="yellow_0.html#T25" onmouseover="rs('yellow_0/T25')" onmouseout="rh()">YELLOW_0:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_2_3_10_2_1_25"><span class="kw">suppose </span></a><a NAME="E1:13_2_3_10_2_1_25"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_2_3_10_2_1_25"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>


</div><span class="kw">end;</span></div>
<span class="kw">take </span>
<font color="Maroon" title="c18">f</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="waybel_1.html#D8" onmouseover="rs('waybel_1/D8')" onmouseout="rh()">WAYBEL_1:def 8</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c18">f</font> is  <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a> </span><br/>

<a NAME="E21:13_2_3"/>
<font color="Maroon" title="c18">f</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">V13</a>()
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_3"><span class="lab"><font color="Green" title="E30">A124</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E22:13_2_3"/>
<font color="Maroon" title="c18">f</font> is  <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:13_2"><span class="lab"><font color="Green" title="E21">A68</font></span></a>, <a class="txt" href="#E19:13_2_3"><span class="lab"><font color="Green" title="E33">A156</font></span></a>, <a class="txt" href="#E20:13_2_3"><span class="lab"><font color="Green" title="E34">A157</font></span></a>, <a class="ref" href="waybel_0.html#T66" onmouseover="rs('waybel_0/T66')" onmouseout="rh()">WAYBEL_0:66</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>


</div><span class="kw">end;</span></div>


</div>
