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<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</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">  for <font color="Olive" title="b1">S</font> being   <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>   <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of  <a href="yellow_1.html#K1" title="YELLOW_1:func.1">InclPoset</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">Y</font><br/>  for <font color="Olive" title="b2">W1</font>, <font color="Olive" title="b3">W2</font> being   <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span>  st <font color="Olive" title="b2">W1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">W2</font> holds <br/> for <font color="Olive" title="b4">f1</font>, <font color="Olive" title="b5">f2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">S</font>)</span>)</span>  st <font color="Olive" title="b4">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b2">W1</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>) <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</a>  &amp; <font color="Olive" title="b5">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">W2</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>) <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</a>  holds <br/><font color="Olive" title="b4">f1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b5">f2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">S</font> be   <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>   <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of  <a href="yellow_1.html#K1" title="YELLOW_1:func.1">InclPoset</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">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">  for <font color="Olive" title="b1">W1</font>, <font color="Olive" title="b2">W2</font> being   <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span>  st <font color="Olive" title="b1">W1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">W2</font> holds <br/> for <font color="Olive" title="b3">f1</font>, <font color="Olive" title="b4">f2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">S</font>)</span>)</span>  st <font color="Olive" title="b3">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b1">W1</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>) <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</a>  &amp; <font color="Olive" title="b4">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b2">W2</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>) <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</a>  holds <br/><font color="Olive" title="b3">f1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b4">f2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">W1</font>, <font color="Maroon" title="c5">W2</font> be   <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.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"> ( <font color="Maroon" title="c4">W1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">W2</font> implies  for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">S</font>)</span>)</span>  st <font color="Olive" title="b1">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c4">W1</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>) <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</a>  &amp; <font color="Olive" title="b2">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c5">W2</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>) <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</a>  holds <br/><font color="Olive" title="b1">f1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b2">f2</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:59"/><span class="lab"><font color="Green" title="E47">A1</font></span>: 
<font color="Maroon" title="c4">W1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">W2</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">  for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">S</font>)</span>)</span>  st <font color="Olive" title="b1">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c4">W1</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>) <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</a>  &amp; <font color="Olive" title="b2">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c5">W2</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>) <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</a>  holds <br/><font color="Olive" title="b1">f1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b2">f2</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">f1</font>, <font color="Maroon" title="c7">f2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">S</font>)</span>)</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="c6">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c4">W1</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>) <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</a>  &amp; <font color="Maroon" title="c7">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c5">W2</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>) <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</a>  implies <font color="Maroon" title="c6">f1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">f2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:59"/><span class="lab"><font color="Green" title="E48">A2</font></span>: 
( <font color="Maroon" title="c6">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c4">W1</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>) <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</a>  &amp; <font color="Maroon" title="c7">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c5">W2</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>) <a href="waybel26.html#K6" title="WAYBEL26:func.6">*graph</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="c6">f1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">f2</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c8">g1</font> = <font color="Maroon" title="c6">f1</font>, <font color="Maroon" title="c9">g2</font> = <font color="Maroon" title="c7">f2</font> as   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">S</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel26.html#T1" target="_self" onmouseover="rs('waybel26/T1')" onmouseout="rh()">Th1</a></span>;<br/>
<a NAME="E4:59"/>
<font color="Maroon" title="c3">S</font> is    <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Maroon" title="c3">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_9.html#T44" onmouseover="rs('yellow_9/T44')" onmouseout="rh()">YELLOW_9:44</a></span>;<br/>
<a NAME="E5:59"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A3</font></span>: 
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">S</font>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">S</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">S</font></span>)</span>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">S</font></span>)</span> #)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel25.html#T16" onmouseover="rs('waybel25/T16')" onmouseout="rh()">WAYBEL25:16</a></span>;<br/>
<a NAME="E6:59"/><span class="lab"><font color="Green" title="E50">A4</font></span>: 
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">S</font>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">S</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</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_1.html#K1" title="YELLOW_1:func.1">InclPoset</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">Y</font></span>)</span>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K1" title="YELLOW_1:func.1">InclPoset</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">Y</font></span>)</span> #)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_9.html#D4" onmouseover="rs('yellow_9/D4')" onmouseout="rh()">YELLOW_9:def 4</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="59_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">  for <font color="Olive" title="b1">j</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">j</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 <font color="Maroon" title="c1">X</font> holds <br/> ex <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">S</font></span>)</span> st <br/>( <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">j</font> &amp; <font color="Olive" title="b3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">g2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">j</font> &amp; <font color="Olive" title="b2">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b3">b</font> )</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c10">j</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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="c10">j</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 <font color="Maroon" title="c1">X</font> implies  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">S</font></span>)</span> st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">j</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">g2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">j</font> &amp; <font color="Olive" title="b1">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b2">b</font> ) )</span><br/><span class="kw">assume </span><a NAME="E1:59_1"/>
<font color="Maroon" title="c10">j</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 <font color="Maroon" title="c1">X</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> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">S</font></span>)</span> st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">j</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">g2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">j</font> &amp; <font color="Olive" title="b1">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b2">b</font> )</span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">x</font> = <font color="Maroon" title="c10">j</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c12">g1x</font> = <font color="Maroon" title="c8">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">x</font>, <font color="Maroon" title="c13">g2x</font> = <font color="Maroon" title="c9">g2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K1" title="YELLOW_1:func.1">InclPoset</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">Y</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:59"><span class="lab"><font color="Green" title="E49">A3</font></span></a>, <a class="ref" href="yellow_9.html#D4" onmouseover="rs('yellow_9/D4')" onmouseout="rh()">YELLOW_9:def 4</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c14">a</font> = <font color="Maroon" title="c8">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">x</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> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">S</font></span>)</span> st <br/>( <font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">j</font> &amp; <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">g2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">j</font> &amp; <font color="Maroon" title="c14">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b1">b</font> )</span><br/><span class="kw">take </span><font color="Maroon" title="c15">b</font> = <font color="Maroon" title="c9">g2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">x</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="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">j</font> &amp; <font color="Maroon" title="c15">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">g2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">j</font> &amp; <font color="Maroon" title="c14">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c15">b</font> )</span><br/><span class="kw">thus </span><a NAME="E4:59_1"/>
( <font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">j</font> &amp; <font color="Maroon" title="c15">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">g2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">j</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="c14">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c15">b</font></span><br/><a NAME="E5:59_1"/>
( <font color="Maroon" title="c8">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K9" title="RELAT_1:func.9">Im</a> (<font color="Maroon" title="c4">W1</font>,<font color="Maroon" title="c11">x</font>) &amp; <font color="Maroon" title="c9">g2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K9" title="RELAT_1:func.9">Im</a> (<font color="Maroon" title="c5">W2</font>,<font color="Maroon" title="c11">x</font>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:59"><span class="lab"><font color="Green" title="E48">A2</font></span></a>, <a class="ref" href="waybel26.html#D5" target="_self" onmouseover="rs('waybel26/D5')" onmouseout="rh()">Def5</a></span>;<br/><a NAME="E6:59_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">g1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">g2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="ref" href="relat_1.html#T124" onmouseover="rs('relat_1/T124')" onmouseout="rh()">RELAT_1:124</a></span>;<br/><a NAME="E7:59_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">g1x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c13">g2x</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="E8:59_1"/>
<font color="Maroon" title="c14">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c15">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:59"><span class="lab"><font color="Green" title="E50">A4</font></span></a>, <a class="txt" href="#E5:59"><span class="lab"><font color="Green" title="E49">A3</font></span></a>, <a class="ref" href="yellow_0.html#T1" onmouseover="rs('yellow_0/T1')" onmouseout="rh()">YELLOW_0:1</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="E8:59"/><span class="kw">then </span>
<font color="Maroon" title="c8">g1</font> <a href="yellow_2.html#R1" title="YELLOW_2:pred.1">&lt;=</a> <font color="Maroon" title="c9">g2</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E9:59"/>
<font color="Maroon" title="c6">f1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">f2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel26.html#T3" target="_self" onmouseover="rs('waybel26/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/>


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