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<span class="kw">let </span><font color="Maroon" title="c1">M</font> be   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> ; <a class="txt" onmouseover="tooltip.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">F</font>, <font color="Olive" title="b2">G</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">F</font> <a href="zfmodel1.html#R2" title="ZFMODEL1:pred.2">is_parametrically_definable_in</a> <font color="Maroon" title="c1">M</font> &amp; <font color="Olive" title="b2">G</font> <a href="zfmodel1.html#R2" title="ZFMODEL1:pred.2">is_parametrically_definable_in</a> <font color="Maroon" title="c1">M</font> holds <br/><font color="Olive" title="b2">G</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b1">F</font> <a href="zfmodel1.html#R2" title="ZFMODEL1:pred.2">is_parametrically_definable_in</a> <font color="Maroon" title="c1">M</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">F</font>, <font color="Maroon" title="c3">G</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</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="c2">F</font> <a href="zfmodel1.html#R2" title="ZFMODEL1:pred.2">is_parametrically_definable_in</a> <font color="Maroon" title="c1">M</font> &amp; <font color="Maroon" title="c3">G</font> <a href="zfmodel1.html#R2" title="ZFMODEL1:pred.2">is_parametrically_definable_in</a> <font color="Maroon" title="c1">M</font> implies <font color="Maroon" title="c3">G</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c2">F</font> <a href="zfmodel1.html#R2" title="ZFMODEL1:pred.2">is_parametrically_definable_in</a> <font color="Maroon" title="c1">M</font> )</span><br/>





<span class="kw">given </span><font color="Maroon" title="c4">H1</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>, <font color="Maroon" title="c5">v1</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>,<font color="Maroon" title="c1">M</font><span class="kw"> such that </span><a NAME="E2:22"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
<span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 2</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H1</font>
 <span class="kw">and </span><br/><a NAME="E3:22"/><span class="lab"><font color="Green" title="E21">A2</font></span>: 
<font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c5">v1</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K12" title="ZF_LANG:func.12">Ex</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">H1</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&lt;=&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>)
 <span class="kw">and </span><br/><a NAME="E4:22"/><span class="lab"><font color="Green" title="E22">A3</font></span>: 
<font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c4">H1</font>,<font color="Maroon" title="c5">v1</font>)
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="zfmodel1.html#D4" onmouseover="rs('zfmodel1/D4')" onmouseout="rh()">ZFMODEL1:def 4</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="c3">G</font> <a href="zfmodel1.html#R2" title="ZFMODEL1:pred.2">is_parametrically_definable_in</a> <font color="Maroon" title="c1">M</font> or <font color="Maroon" title="c3">G</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c2">F</font> <a href="zfmodel1.html#R2" title="ZFMODEL1:pred.2">is_parametrically_definable_in</a> <font color="Maroon" title="c1">M</font> )</span><br/>

<span class="kw">given </span><font color="Maroon" title="c6">H2</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>, <font color="Maroon" title="c7">v2</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>,<font color="Maroon" title="c1">M</font><span class="kw"> such that </span><a NAME="E6:22"/><span class="lab"><font color="Green" title="E23">A4</font></span>: 
<span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 2</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</font>
 <span class="kw">and </span><br/><a NAME="E7:22"/><span class="lab"><font color="Green" title="E24">A5</font></span>: 
<font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c7">v2</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K12" title="ZF_LANG:func.12">Ex</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">H2</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&lt;=&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>)
 <span class="kw">and </span><br/><a NAME="E8:22"/><span class="lab"><font color="Green" title="E25">A6</font></span>: 
<font color="Maroon" title="c3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c6">H2</font>,<font color="Maroon" title="c7">v2</font>)
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="zfmodel1.html#D4" onmouseover="rs('zfmodel1/D4')" onmouseout="rh()">ZFMODEL1:def 4</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="c3">G</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c2">F</font> <a href="zfmodel1.html#R2" title="ZFMODEL1:pred.2">is_parametrically_definable_in</a> <font color="Maroon" title="c1">M</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c8">F9</font> = <font color="Maroon" title="c2">F</font>, <font color="Maroon" title="c9">G9</font> = <font color="Maroon" title="c3">G</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c1">M</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="txt" href="#E8:22"><span class="lab"><font color="Green" title="E25">A6</font></span></a></span>;<br/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ) <span class="kw">-&gt; </span>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  = <font color="Maroon" title="c7">v2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1;<br/>
<span class="kw">consider </span><font color="Maroon" title="c10">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <span class="kw"> such that </span><br/><a NAME="E11:22"/><span class="lab"><font color="Green" title="E26">A7</font></span>: 
 for <font color="Olive" title="b1">j</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Olive" title="b1">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Maroon" title="c6">H2</font> holds <br/><font color="Olive" title="b1">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c10">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmodel2.html#T3" target="_self" onmouseover="rs('zfmodel2/T3')" onmouseout="rh()">Th3</a></span>;<br/>
<a NAME="E12:22"/>
( <font color="Maroon" title="c10">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 4 or  not <font color="Maroon" title="c10">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 4 )
 
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">i3</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <span class="kw"> such that </span><br/><a NAME="E14:22"/><span class="lab"><font color="Green" title="E27">A8</font></span>: 
( ( <font color="Maroon" title="c10">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 4 &amp; <font color="Maroon" title="c11">i3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">i</font> ) or (  not <font color="Maroon" title="c10">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 4 &amp; <font color="Maroon" title="c11">i3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 ) )
 ;<br/>
<a NAME="E15:22"/><span class="lab"><font color="Green" title="E28">A9</font></span>: 
 <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 2</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</a></span>;<br/>
<a NAME="E16:22"/><span class="kw">then </span>
 not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="xboole_0.html#T3" onmouseover="rs('xboole_0/T3')" onmouseout="rh()">XBOOLE_0:3</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">H3</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>, <font color="Maroon" title="c13">v3</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>,<font color="Maroon" title="c1">M</font><span class="kw"> such that </span><br/><a NAME="E18:22"/><span class="lab"><font color="Green" title="E29">A10</font></span>: 
 for <font color="Olive" title="b1">j</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b1">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c11">i3</font> &amp;  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Olive" title="b1">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Maroon" title="c12">H3</font> &amp;  not <font color="Olive" title="b1">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 holds <br/><font color="Olive" title="b1">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 <span class="kw">and </span><br/><a NAME="E19:22"/><span class="lab"><font color="Green" title="E30">A11</font></span>: 
 not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font>
 <span class="kw">and </span><br/><a NAME="E20:22"/><span class="lab"><font color="Green" title="E31">A12</font></span>: 
<font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c13">v3</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K12" title="ZF_LANG:func.12">Ex</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">H3</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&lt;=&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>)
 <span class="kw">and </span><br/><a NAME="E21:22"/><span class="lab"><font color="Green" title="E32">A13</font></span>: 
 <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c4">H1</font>,<font color="Maroon" title="c5">v1</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c12">H3</font>,<font color="Maroon" title="c13">v3</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="zfmodel2.html#T16" target="_self" onmouseover="rs('zfmodel2/T16')" onmouseout="rh()">Th16</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c14">k1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <span class="kw"> such that </span><br/><a NAME="E23:22"/><span class="lab"><font color="Green" title="E33">A14</font></span>: 
 for <font color="Olive" title="b1">j</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Olive" title="b1">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Maroon" title="c12">H3</font> holds <br/><font color="Olive" title="b1">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c14">k1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmodel2.html#T3" target="_self" onmouseover="rs('zfmodel2/T3')" onmouseout="rh()">Th3</a></span>;<br/>
<a NAME="E24:22"/>
( <font color="Maroon" title="c14">k1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c11">i3</font> or <font color="Maroon" title="c14">k1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">i3</font> )
 
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c15">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <span class="kw"> such that </span><br/><a NAME="E26:22"/><span class="lab"><font color="Green" title="E34">A15</font></span>: 
( ( <font color="Maroon" title="c14">k1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c11">i3</font> &amp; <font color="Maroon" title="c15">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">k1</font> ) or ( <font color="Maroon" title="c14">k1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">i3</font> &amp; <font color="Maroon" title="c15">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">i3</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 ) )
 ;<br/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>2</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ) <span class="kw">-&gt; </span>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  = <font color="Maroon" title="c13">v3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1;<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> ] <span class="kw">means </span>$1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font>;<br/>
<span class="kw">take </span><font color="Maroon" title="c16">H</font> =  <a href="zf_lang.html#K12" title="ZF_LANG:func.12">Ex</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span> <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span></span>)</span>); <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="zfmodel1.html#D4" onmouseover="rs('zfmodel1/D4')" onmouseout="rh()">ZFMODEL1:def 4</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">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">K27</a>(<a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">K28</a>(<a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>,<font color="Maroon" title="c1">M</font>)) st <br/>( <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 2</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c16">H</font> &amp; <font color="Maroon" title="c1">M</font>,<font color="Olive">b<sub>1</sub></font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K12" title="ZF_LANG:func.12">Ex</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c16">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&lt;=&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>) &amp; <font color="Maroon" title="c3">G</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Olive">b<sub>1</sub></font>) )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c17">v</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E28:22"/><span class="lab"><font color="Green" title="E35">A16</font></span>: 
(  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c17">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>  &amp; (  for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>  holds <br/>( ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">a</font>] implies <font color="Maroon" title="c17">v</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive" title="b1">a</font>) ) &amp; (  not <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">a</font>] implies <font color="Maroon" title="c17">v</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">a</font>) ) ) ) )
 <span class="kw">from</span> <span class="lab"><a class="ref" href="partfun1.html#S1" onmouseover="rs('partfun1/S1')" onmouseout="rh()">PARTFUN1:sch 1</a>();<br/></span>
<a NAME="E29:22"/>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c17">v</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">M</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c18">b</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="c18">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c17">v</font> or <font color="Maroon" title="c18">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">M</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:22_1"/>
<font color="Maroon" title="c18">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c17">v</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">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">M</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c19">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:22_1"/><span class="lab"><font color="Green" title="E36">A17</font></span>: 
<font color="Maroon" title="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c17">v</font>
 <span class="kw">and </span><br/><a NAME="E4:22_1"/><span class="lab"><font color="Green" title="E37">A18</font></span>: 
<font color="Maroon" title="c18">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">v</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">a</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="c20">a</font> = <font color="Maroon" title="c19">a</font> as   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:22"><span class="lab"><font color="Green" title="E35">A16</font></span></a>, <a class="txt" href="#E3:22_1"><span class="lab"><font color="Green" title="E36">A17</font></span></a></span>;<br/>
<a NAME="E6:22_1"/>
( <font color="Maroon" title="c18">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">v3</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">a</font> or <font color="Maroon" title="c18">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">a</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:22"><span class="lab"><font color="Green" title="E35">A16</font></span></a>, <a class="txt" href="#E4:22_1"><span class="lab"><font color="Green" title="E37">A18</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:22_1"/>
<font color="Maroon" title="c18">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">M</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>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c18">v</font> = <font color="Maroon" title="c17">v</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a>,<font color="Maroon" title="c1">M</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:22"><span class="lab"><font color="Green" title="E35">A16</font></span></a>, <a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T4" onmouseover="rs('relset_1/T4')" onmouseout="rh()">RELSET_1:4</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c18">v</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"> ( <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 2</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c16">H</font> &amp; <font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c18">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K12" title="ZF_LANG:func.12">Ex</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c16">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&lt;=&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>) &amp; <font color="Maroon" title="c3">G</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>) )</span><br/>

<a NAME="E31:22"/><span class="lab"><font color="Green" title="E36">A19</font></span>: 
<span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 2</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:22_2"/><span class="lab"><font color="Green" title="E37">A20</font></span>: 
<font color="Maroon" title="c11">i3</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:22"><span class="lab"><font color="Green" title="E27">A8</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<a NAME="E2:22_2"/><span class="lab"><font color="Green" title="E38">A21</font></span>: 
<font color="Maroon" title="c11">i3</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:22"><span class="lab"><font color="Green" title="E27">A8</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:22_2"/>
<span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 2</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</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/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c19">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E5:22_2"/><span class="lab"><font color="Green" title="E39">A22</font></span>: 
<font color="Maroon" title="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 2</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 <span class="kw">and </span><br/><a NAME="E6:22_2"/><span class="lab"><font color="Green" title="E40">A23</font></span>: 
<font color="Maroon" title="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#T3" onmouseover="rs('xboole_0/T3')" onmouseout="rh()">XBOOLE_0:3</a></span>;<br/>
<a NAME="E7:22_2"/><span class="lab"><font color="Green" title="E41">A24</font></span>: 
 <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Maroon" title="c12">H3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T151" onmouseover="rs('zf_lang1/T151')" onmouseout="rh()">ZF_LANG1:151</a></span>;<br/>
<a NAME="E8:22_2"/>
( <font color="Maroon" title="c19">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> or <font color="Maroon" title="c19">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 1 or <font color="Maroon" title="c19">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 2 )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22_2"><span class="lab"><font color="Green" title="E39">A22</font></span></a>, <a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:22_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:22"><span class="lab"><font color="Green" title="E29">A10</font></span></a>, <a class="txt" href="#E2:22_2"><span class="lab"><font color="Green" title="E38">A21</font></span></a>, <a class="txt" href="#E1:22_2"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="txt" href="#E6:22_2"><span class="lab"><font color="Green" title="E40">A23</font></span></a>, <a class="txt" href="#E7:22_2"><span class="lab"><font color="Green" title="E41">A24</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="E37">A25</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_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">  for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 2</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> holds <br/> not <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c16">H</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">a</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="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 2</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> implies  not <font color="Maroon" title="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c16">H</font> )</span><br/><span class="kw">assume </span><a NAME="E1:22_3"/><span class="lab"><font color="Green" title="E38">A26</font></span>: 
<font color="Maroon" title="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 2</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.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="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c16">H</font></span><br/><span class="kw">assume </span><a NAME="E2:22_3"/>
<font color="Maroon" title="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c16">H</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="E3:22_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A27</font></span>: 
<font color="Maroon" title="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span> <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T66" onmouseover="rs('zf_lang1/T66')" onmouseout="rh()">ZF_LANG1:66</a></span>;<br/><a NAME="E4:22_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A28</font></span>: 
 not <font color="Maroon" title="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" onmouseover="rs('xboole_0/D5')" onmouseout="rh()">XBOOLE_0:def 5</a></span>;<br/><a NAME="E5:22_3"/><span class="lab"><font color="Green" title="E41">A29</font></span>: 
 <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span> <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T61" onmouseover="rs('zf_lang1/T61')" onmouseout="rh()">ZF_LANG1:61</a></span>;<br/><a NAME="E6:22_3"/>
<font color="Maroon" title="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span> <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_3"><span class="lab"><font color="Green" title="E39">A27</font></span></a>, <a class="ref" href="xboole_0.html#D5" onmouseover="rs('xboole_0/D5')" onmouseout="rh()">XBOOLE_0:def 5</a></span>;<br/><a NAME="E7:22_3"/><span class="kw">then </span>
( (  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span> ) or ( <font color="Maroon" title="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span> &amp;  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22_3"><span class="lab"><font color="Green" title="E41">A29</font></span></a>, <a class="ref" href="zfmodel2.html#T1" target="_self" onmouseover="rs('zfmodel2/T1')" onmouseout="rh()">Th1</a>, <a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>;<br/><a NAME="E8:22_3"/><span class="kw">then </span>
( <font color="Maroon" title="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> or <font color="Maroon" title="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_3"><span class="lab"><font color="Green" title="E40">A28</font></span></a>, <a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>;<br/><a NAME="E9:22_3"/><span class="kw">then </span>
( <font color="Maroon" title="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font> or <font color="Maroon" title="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" onmouseover="rs('xboole_0/D5')" onmouseout="rh()">XBOOLE_0:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E10:22_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:22"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="txt" href="#E31:22"><span class="lab"><font color="Green" title="E36">A19</font></span></a>, <a class="txt" href="#E1:22_3"><span class="lab"><font color="Green" title="E38">A26</font></span></a>, <a class="ref" href="xboole_0.html#T3" onmouseover="rs('xboole_0/T3')" onmouseout="rh()">XBOOLE_0:3</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">hence </span><a NAME="E33:22"/>
<span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 2</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c16">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#T3" onmouseover="rs('xboole_0/T3')" onmouseout="rh()">XBOOLE_0:3</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" title="c1">M</font>,<font color="Maroon" title="c18">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K12" title="ZF_LANG:func.12">Ex</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c16">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&lt;=&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>) &amp; <font color="Maroon" title="c3">G</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>) )</span><br/>

<a NAME="E34:22"/>
 <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 2</span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</a></span>;<br/>
<a NAME="E35:22"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A30</font></span>: 
 not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c16">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:22"><span class="lab"><font color="Green" title="E37">A25</font></span></a></span>;<br/>
<a NAME="E36:22"/><span class="lab"><font color="Green" title="E39">A31</font></span>: 
<font color="Maroon" title="c15">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 4
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:22"><span class="lab"><font color="Green" title="E27">A8</font></span></a>, <a class="txt" href="#E26:22"><span class="lab"><font color="Green" title="E34">A15</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E37:22"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A32</font></span>: 
 <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a></span>;<br/>
<a NAME="E38:22"/><span class="lab"><font color="Green" title="E41">A33</font></span>: 
<font color="Maroon" title="c10">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">i3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:22"><span class="lab"><font color="Green" title="E27">A8</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<a NAME="E39:22"/><span class="lab"><font color="Green" title="E42">A34</font></span>: 
 not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Maroon" title="c6">H2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:22_4"/>
 <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Maroon" title="c6">H2</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="E2:22_4"/><span class="kw">then </span>
<font color="Maroon" title="c15">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c10">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:22"><span class="lab"><font color="Green" title="E26">A7</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:22_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:22"><span class="lab"><font color="Green" title="E41">A33</font></span></a>, <a class="txt" href="#E26:22"><span class="lab"><font color="Green" title="E34">A15</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</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="E40:22"/><span class="lab"><font color="Green" title="E43">A35</font></span>: 
 for <font color="Olive" title="b1">x</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  holds <br/>(  not <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</font> or  not <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font> or <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 or <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c19">x</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</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">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</font> or  not <font color="Maroon" title="c19">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font> or <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 or <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 )</span><br/>

<a NAME="E1:22_5"/><span class="lab"><font color="Green" title="E44">A36</font></span>: 
 <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Maroon" title="c12">H3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T151" onmouseover="rs('zf_lang1/T151')" onmouseout="rh()">ZF_LANG1:151</a></span>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:22_5"/><span class="lab"><font color="Green" title="E45">A37</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</font>
 <span class="kw">and </span><br/><a NAME="E3:22_5"/><span class="lab"><font color="Green" title="E46">A38</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</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>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 or <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c20">j</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <span class="kw"> such that </span><br/><a NAME="E5:22_5"/><span class="lab"><font color="Green" title="E47">A39</font></span>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c20">j</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T77" onmouseover="rs('zf_lang1/T77')" onmouseout="rh()">ZF_LANG1:77</a></span>;<br/>
<a NAME="E6:22_5"/>
 <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Maroon" title="c6">H2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T151" onmouseover="rs('zf_lang1/T151')" onmouseout="rh()">ZF_LANG1:151</a></span>;<br/>
<a NAME="E7:22_5"/><span class="kw">then </span>
<font color="Maroon" title="c20">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c11">i3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:22"><span class="lab"><font color="Green" title="E26">A7</font></span></a>, <a class="txt" href="#E38:22"><span class="lab"><font color="Green" title="E41">A33</font></span></a>, <a class="txt" href="#E5:22_5"><span class="lab"><font color="Green" title="E47">A39</font></span></a>, <a class="txt" href="#E2:22_5"><span class="lab"><font color="Green" title="E45">A37</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:22_5"/>
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 or <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:22"><span class="lab"><font color="Green" title="E29">A10</font></span></a>, <a class="txt" href="#E1:22_5"><span class="lab"><font color="Green" title="E44">A36</font></span></a>, <a class="txt" href="#E5:22_5"><span class="lab"><font color="Green" title="E47">A39</font></span></a>, <a class="txt" href="#E3:22_5"><span class="lab"><font color="Green" title="E46">A38</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>
<a NAME="E41:22"/><span class="lab"><font color="Green" title="E44">A40</font></span>: 
<font color="Maroon" title="c15">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:22"><span class="lab"><font color="Green" title="E27">A8</font></span></a>, <a class="txt" href="#E26:22"><span class="lab"><font color="Green" title="E34">A15</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<a NAME="E42:22"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A41</font></span>: 
 <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a></span>;<br/>
<a NAME="E43:22"/><span class="lab"><font color="Green" title="E46">A42</font></span>: 
 not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Maroon" title="c12">H3</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:22_6"/>
 <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Maroon" title="c12">H3</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="E2:22_6"/><span class="kw">then </span>
<font color="Maroon" title="c15">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c14">k1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:22"><span class="lab"><font color="Green" title="E33">A14</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:22_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:22"><span class="lab"><font color="Green" title="E34">A15</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</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="E44:22"/><span class="lab"><font color="Green" title="E47">A43</font></span>: 
 not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:22"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="txt" href="#E15:22"><span class="lab"><font color="Green" title="E28">A9</font></span></a>, <a class="ref" href="xboole_0.html#T3" onmouseover="rs('xboole_0/T3')" onmouseout="rh()">XBOOLE_0:3</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_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">m1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</font>  ex <font color="Olive" title="b2">r</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</font> st <br/> for <font color="Olive" title="b3">m3</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</font> holds <br/> ( ( <font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Olive" title="b1">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Olive" title="b3">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c16">H</font> implies <font color="Olive" title="b3">m3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">r</font> ) &amp; ( <font color="Olive" title="b3">m3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">r</font> implies <font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Olive" title="b1">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Olive" title="b3">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c16">H</font> ) )</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">m1</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</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">r</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</font> st <br/> for <font color="Olive" title="b2">m3</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</font> holds <br/> ( ( <font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Olive" title="b2">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c16">H</font> implies <font color="Olive" title="b2">m3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r</font> ) &amp; ( <font color="Olive" title="b2">m3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r</font> implies <font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Olive" title="b2">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c16">H</font> ) )</span><br/><a NAME="E1:22_7"/><span class="lab"><font color="Green" title="E48">A44</font></span>: 
 not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:22"><span class="lab"><font color="Green" title="E44">A40</font></span></a>, <a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a>, <a class="ref" href="zf_lang1.html#T184" onmouseover="rs('zf_lang1/T184')" onmouseout="rh()">ZF_LANG1:184</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c20">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</font><span class="kw"> such that </span><br/><a NAME="E3:22_7"/><span class="lab"><font color="Green" title="E49">A45</font></span>: 
 for <font color="Olive" title="b1">m4</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</font> holds <br/> ( <font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Olive" title="b1">m4</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font> iff <font color="Olive" title="b1">m4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">m</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:22"><span class="lab"><font color="Green" title="E30">A11</font></span></a>, <a class="txt" href="#E20:22"><span class="lab"><font color="Green" title="E31">A12</font></span></a>, <a class="ref" href="zfmodel2.html#T19" target="_self" onmouseover="rs('zfmodel2/T19')" onmouseout="rh()">Th19</a></span>;<br/><div><span class="lab"><font color="Green" title="E50">A46</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_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">  for <font color="Olive" title="b1">x</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c21">x</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</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="c21">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:22_7_1"/><span class="lab"><font color="Green" title="E51">A47</font></span>: 
<font color="Maroon" title="c21">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</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"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font></span><br/><a NAME="E2:22_7_1"/>
 <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmodel2.html#T1" target="_self" onmouseover="rs('zfmodel2/T1')" onmouseout="rh()">Th1</a></span>;<br/><a NAME="E3:22_7_1"/><span class="kw">then </span>
( <font color="Maroon" title="c21">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> or <font color="Maroon" title="c21">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_7_1"><span class="lab"><font color="Green" title="E51">A47</font></span></a>, <a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>;<br/><a NAME="E4:22_7_1"/><span class="kw">then </span>
( ( <font color="Maroon" title="c21">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font> &amp;  not <font color="Maroon" title="c21">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) or <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a>, <a class="ref" href="xboole_0.html#D5" onmouseover="rs('xboole_0/D5')" onmouseout="rh()">XBOOLE_0:def 5</a></span>;<br/><a NAME="E5:22_7_1"/><span class="kw">then </span>
( ( ( ( <font color="Maroon" title="c21">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font> &amp;  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">x</font> &amp; <font color="Maroon" title="c21">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font> ) or <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 or <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 ) &amp; <font color="Maroon" title="c21">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 ) or ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">m</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">m</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><a NAME="E6:22_7_1"/><span class="kw">then </span>
( ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> &amp; <font color="Maroon" title="c18">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">v3</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> &amp; <font color="Maroon" title="c13">v3</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> ) or ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">m1</font> &amp; <font color="Maroon" title="c19">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> ) or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:22"><span class="lab"><font color="Green" title="E45">A41</font></span></a>, <a class="txt" href="#E28:22"><span class="lab"><font color="Green" title="E35">A16</font></span></a>, <a class="ref" href="funct_7.html#T32" onmouseover="rs('funct_7/T32')" onmouseout="rh()">FUNCT_7:32</a>, <a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/><span class="kw">hence </span><a NAME="E7:22_7_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c21">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"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">consider </span><font color="Maroon" title="c21">r</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</font><span class="kw"> such that </span><br/><a NAME="E6:22_7"/><span class="lab"><font color="Green" title="E51">A48</font></span>: 
 for <font color="Olive" title="b1">m4</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</font> holds <br/> ( <font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Olive" title="b1">m4</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font> iff <font color="Olive" title="b1">m4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">r</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:22"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E44:22"><span class="lab"><font color="Green" title="E47">A43</font></span></a>, <a class="ref" href="zfmodel2.html#T19" target="_self" onmouseover="rs('zfmodel2/T19')" onmouseout="rh()">Th19</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c22">r</font> = <font color="Maroon" title="c21">r</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">m3</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</font> holds <br/> ( ( <font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Olive" title="b1">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c16">H</font> implies <font color="Olive" title="b1">m3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">r</font> ) &amp; ( <font color="Olive" title="b1">m3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">r</font> implies <font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Olive" title="b1">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c16">H</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c23">m3</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</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="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c16">H</font> implies <font color="Maroon" title="c23">m3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">r</font> ) &amp; ( <font color="Maroon" title="c23">m3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">r</font> implies <font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c16">H</font> ) )</span><br/><a NAME="E7:22_7"/><span class="lab"><font color="Green" title="E52">A49</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/><span class="kw">thus </span><a NAME="E8:22_7"/>
( <font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c16">H</font> implies <font color="Maroon" title="c23">m3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">r</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="c23">m3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">r</font> implies <font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c16">H</font> )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_7_2"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E53">A50</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_7_2_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">x</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c24">x</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</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="c24">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:22_7_2_1"/>
<font color="Maroon" title="c24">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</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"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font></span><br/><a NAME="E2:22_7_2_1"/><span class="kw">then </span>
( (  not <font color="Maroon" title="c24">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font> &amp; <font color="Maroon" title="c24">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 &amp; <font color="Maroon" title="c24">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 ) or <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 or <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:22"><span class="lab"><font color="Green" title="E43">A35</font></span></a></span>;<br/><a NAME="E3:22_7_2_1"/><span class="kw">then </span>
( ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> &amp; <font color="Maroon" title="c18">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> &amp; <font color="Maroon" title="c7">v2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> ) or ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">m</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">m</font> ) or ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">m3</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">m3</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:22"><span class="lab"><font color="Green" title="E35">A16</font></span></a>, <a class="txt" href="zfmodel2.html#E13"><span class="lab"><font color="Green" title="E13">Lm3</font></span></a>, <a class="ref" href="funct_7.html#T32" onmouseover="rs('funct_7/T32')" onmouseout="rh()">FUNCT_7:32</a>, <a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/><span class="kw">hence </span><a NAME="E4:22_7_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">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"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:22_7_2"/>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c16">H</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="c23">m3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">r</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c24">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</font><span class="kw"> such that </span><br/><a NAME="E4:22_7_2"/><span class="lab"><font color="Green" title="E54">A51</font></span>: 
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c24">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span> <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T73" onmouseover="rs('zf_lang1/T73')" onmouseout="rh()">ZF_LANG1:73</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E55">A52</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_7_2_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">  for <font color="Olive" title="b1">x</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c25">x</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</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="c25">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:22_7_2_2"/><span class="lab"><font color="Green" title="E56">A53</font></span>: 
<font color="Maroon" title="c25">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</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"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">x</font></span><br/><a NAME="E2:22_7_2_2"/><span class="lab"><font color="Green" title="E57">A54</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/><a NAME="E3:22_7_2_2"/><span class="lab"><font color="Green" title="E58">A55</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T32" onmouseover="rs('funct_7/T32')" onmouseout="rh()">FUNCT_7:32</a>, <a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a></span>;<br/><a NAME="E4:22_7_2_2"/><span class="lab"><font color="Green" title="E59">A56</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T32" onmouseover="rs('funct_7/T32')" onmouseout="rh()">FUNCT_7:32</a>, <a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a></span>;<br/><a NAME="E5:22_7_2_2"/><span class="lab"><font color="Green" title="E60">A57</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">m1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/><a NAME="E6:22_7_2_2"/>
( <font color="Maroon" title="c25">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 or <font color="Maroon" title="c25">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 or ( <font color="Maroon" title="c25">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 &amp; <font color="Maroon" title="c25">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 ) )
 ;<br/><a NAME="E7:22_7_2_2"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">x</font> or ( <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">v3</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">x</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">x</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">x</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_7_2_2"><span class="lab"><font color="Green" title="E57">A54</font></span></a>, <a class="txt" href="#E5:22_7_2_2"><span class="lab"><font color="Green" title="E60">A57</font></span></a>, <a class="txt" href="#E4:22_7_2_2"><span class="lab"><font color="Green" title="E59">A56</font></span></a>, <a class="txt" href="#E3:22_7_2_2"><span class="lab"><font color="Green" title="E58">A55</font></span></a>, <a class="ref" href="funct_7.html#T32" onmouseover="rs('funct_7/T32')" onmouseout="rh()">FUNCT_7:32</a>, <a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/><span class="kw">hence </span><a NAME="E8:22_7_2_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:22"><span class="lab"><font color="Green" title="E35">A16</font></span></a>, <a class="txt" href="#E1:22_7_2_2"><span class="lab"><font color="Green" title="E56">A53</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>
<a NAME="E6:22_7_2"/><span class="lab"><font color="Green" title="E56">A58</font></span>: 
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c24">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_7_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="ref" href="zf_model.html#T15" onmouseover="rs('zf_model/T15')" onmouseout="rh()">ZF_MODEL:15</a></span>;<br/>
<a NAME="E7:22_7_2"/><span class="lab"><font color="Green" title="E57">A59</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/>
<a NAME="E8:22_7_2"/>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c24">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_7_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="ref" href="zf_model.html#T15" onmouseover="rs('zf_model/T15')" onmouseout="rh()">ZF_MODEL:15</a></span>;<br/>
<a NAME="E9:22_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:22"><span class="lab"><font color="Green" title="E46">A42</font></span></a>, <a class="txt" href="#E7:22_7_2"><span class="lab"><font color="Green" title="E57">A59</font></span></a>, <a class="ref" href="zfmodel2.html#T12" target="_self" onmouseover="rs('zfmodel2/T12')" onmouseout="rh()">Th12</a></span>;<br/>
<a NAME="E10:22_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmodel2.html#T8" target="_self" onmouseover="rs('zfmodel2/T8')" onmouseout="rh()">Th8</a></span>;<br/>
<a NAME="E11:22_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c24">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:22"><span class="lab"><font color="Green" title="E39">A31</font></span></a>, <a class="ref" href="funct_7.html#T33" onmouseover="rs('funct_7/T33')" onmouseout="rh()">FUNCT_7:33</a>, <a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a></span>;<br/>
<a NAME="E12:22_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:22"><span class="lab"><font color="Green" title="E46">A42</font></span></a>, <a class="ref" href="zfmodel2.html#T5" target="_self" onmouseover="rs('zfmodel2/T5')" onmouseout="rh()">Th5</a></span>;<br/>
<a NAME="E13:22_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c24">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22_7_2"><span class="lab"><font color="Green" title="E55">A52</font></span></a>, <a class="ref" href="zf_lang1.html#T75" onmouseover="rs('zf_lang1/T75')" onmouseout="rh()">ZF_LANG1:75</a></span>;<br/>
<a NAME="E14:22_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c24">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_7"><span class="lab"><font color="Green" title="E49">A45</font></span></a></span>;<br/>
<a NAME="E15:22_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:22"><span class="lab"><font color="Green" title="E42">A34</font></span></a>, <a class="txt" href="#E7:22_7_2"><span class="lab"><font color="Green" title="E57">A59</font></span></a>, <a class="txt" href="#E6:22_7_2"><span class="lab"><font color="Green" title="E56">A58</font></span></a>, <a class="ref" href="zfmodel2.html#T12" target="_self" onmouseover="rs('zfmodel2/T12')" onmouseout="rh()">Th12</a></span>;<br/>
<a NAME="E16:22_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmodel2.html#T8" target="_self" onmouseover="rs('zfmodel2/T8')" onmouseout="rh()">Th8</a></span>;<br/>
<a NAME="E17:22_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:22"><span class="lab"><font color="Green" title="E45">A41</font></span></a>, <a class="txt" href="#E37:22"><span class="lab"><font color="Green" title="E40">A32</font></span></a>, <a class="txt" href="zfmodel2.html#E13"><span class="lab"><font color="Green" title="E13">Lm3</font></span></a>, <a class="ref" href="zfmodel2.html#T6" target="_self" onmouseover="rs('zfmodel2/T6')" onmouseout="rh()">Th6</a></span>;<br/>
<a NAME="E18:22_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:22"><span class="lab"><font color="Green" title="E42">A34</font></span></a>, <a class="ref" href="zfmodel2.html#T5" target="_self" onmouseover="rs('zfmodel2/T5')" onmouseout="rh()">Th5</a></span>;<br/>
<a NAME="E19:22_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_7_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="ref" href="zf_lang1.html#T75" onmouseover="rs('zf_lang1/T75')" onmouseout="rh()">ZF_LANG1:75</a></span>;<br/>
<span class="kw">hence </span><a NAME="E20:22_7_2"/>
<font color="Maroon" title="c23">m3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">r</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:22_7"><span class="lab"><font color="Green" title="E51">A48</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">assume </span><a NAME="E9:22_7"/>
<font color="Maroon" title="c23">m3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">r</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="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c16">H</font></span><br/><a NAME="E10:22_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A60</font></span>: 
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:22_7"><span class="lab"><font color="Green" title="E51">A48</font></span></a></span>;<br/><a NAME="E11:22_7"/><span class="lab"><font color="Green" title="E54">A61</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/><div><span class="lab"><font color="Green" title="E55">A62</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_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">  for <font color="Olive" title="b1">x</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c24">x</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</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="c24">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:22_7_3"/><span class="lab"><font color="Green" title="E56">A63</font></span>: 
<font color="Maroon" title="c24">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</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"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font></span><br/><a NAME="E2:22_7_3"/>
 <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmodel2.html#T1" target="_self" onmouseover="rs('zfmodel2/T1')" onmouseout="rh()">Th1</a></span>;<br/><a NAME="E3:22_7_3"/><span class="kw">then </span>
( <font color="Maroon" title="c24">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> or <font color="Maroon" title="c24">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_7_3"><span class="lab"><font color="Green" title="E56">A63</font></span></a>, <a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>;<br/><a NAME="E4:22_7_3"/><span class="kw">then </span>
( ( <font color="Maroon" title="c24">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</font> &amp;  not <font color="Maroon" title="c24">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) or <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a>, <a class="ref" href="xboole_0.html#D5" onmouseover="rs('xboole_0/D5')" onmouseout="rh()">XBOOLE_0:def 5</a></span>;<br/><a NAME="E5:22_7_3"/><span class="kw">then </span>
( ( ( (  not <font color="Maroon" title="c24">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font> &amp;  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">x</font> &amp; <font color="Maroon" title="c24">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font> ) or <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 or <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 ) &amp; <font color="Maroon" title="c24">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 ) or ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">m</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">m</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:22"><span class="lab"><font color="Green" title="E43">A35</font></span></a>, <a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><a NAME="E6:22_7_3"/><span class="kw">then </span>
( ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> &amp; <font color="Maroon" title="c18">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> &amp; <font color="Maroon" title="c7">v2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> ) or ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">m3</font> &amp; <font color="Maroon" title="c23">m3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> ) or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:22"><span class="lab"><font color="Green" title="E40">A32</font></span></a>, <a class="txt" href="#E28:22"><span class="lab"><font color="Green" title="E35">A16</font></span></a>, <a class="ref" href="funct_7.html#T32" onmouseover="rs('funct_7/T32')" onmouseout="rh()">FUNCT_7:32</a>, <a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/><span class="kw">hence </span><a NAME="E7:22_7_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">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"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E13:22_7"/><span class="lab"><font color="Green" title="E56">A64</font></span>: 
 not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:22"><span class="lab"><font color="Green" title="E39">A31</font></span></a>, <a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a>, <a class="ref" href="zf_lang1.html#T184" onmouseover="rs('zf_lang1/T184')" onmouseout="rh()">ZF_LANG1:184</a></span>;<br/><a NAME="E14:22_7"/>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c20">m</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_7"><span class="lab"><font color="Green" title="E49">A45</font></span></a></span>;<br/><a NAME="E15:22_7"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:22"><span class="lab"><font color="Green" title="E46">A42</font></span></a>, <a class="txt" href="#E7:22_7"><span class="lab"><font color="Green" title="E52">A49</font></span></a>, <a class="ref" href="zfmodel2.html#T13" target="_self" onmouseover="rs('zfmodel2/T13')" onmouseout="rh()">Th13</a></span>;<br/><a NAME="E16:22_7"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c20">m</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:22"><span class="lab"><font color="Green" title="E39">A31</font></span></a>, <a class="ref" href="funct_7.html#T33" onmouseover="rs('funct_7/T33')" onmouseout="rh()">FUNCT_7:33</a>, <a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a></span>;<br/><a NAME="E17:22_7"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:22_7"><span class="lab"><font color="Green" title="E56">A64</font></span></a>, <a class="ref" href="zfmodel2.html#T5" target="_self" onmouseover="rs('zfmodel2/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E18:22_7"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_7"><span class="lab"><font color="Green" title="E50">A46</font></span></a>, <a class="ref" href="zf_lang1.html#T75" onmouseover="rs('zf_lang1/T75')" onmouseout="rh()">ZF_LANG1:75</a></span>;<br/><a NAME="E19:22_7"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:22_7"><span class="lab"><font color="Green" title="E56">A64</font></span></a>, <a class="ref" href="zfmodel2.html#T5" target="_self" onmouseover="rs('zfmodel2/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E20:22_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A65</font></span>: 
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:22"><span class="lab"><font color="Green" title="E39">A31</font></span></a>, <a class="ref" href="funct_7.html#T33" onmouseover="rs('funct_7/T33')" onmouseout="rh()">FUNCT_7:33</a>, <a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a></span>;<br/><a NAME="E21:22_7"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T32" onmouseover="rs('funct_7/T32')" onmouseout="rh()">FUNCT_7:32</a>, <a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a></span>;<br/><a NAME="E22:22_7"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:22"><span class="lab"><font color="Green" title="E42">A34</font></span></a>, <a class="txt" href="#E11:22_7"><span class="lab"><font color="Green" title="E54">A61</font></span></a>, <a class="txt" href="#E10:22_7"><span class="lab"><font color="Green" title="E53">A60</font></span></a>, <a class="ref" href="zfmodel2.html#T13" target="_self" onmouseover="rs('zfmodel2/T13')" onmouseout="rh()">Th13</a></span>;<br/><a NAME="E23:22_7"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:22"><span class="lab"><font color="Green" title="E45">A41</font></span></a>, <a class="txt" href="#E37:22"><span class="lab"><font color="Green" title="E40">A32</font></span></a>, <a class="txt" href="zfmodel2.html#E13"><span class="lab"><font color="Green" title="E13">Lm3</font></span></a>, <a class="ref" href="zfmodel2.html#T6" target="_self" onmouseover="rs('zfmodel2/T6')" onmouseout="rh()">Th6</a></span>;<br/><a NAME="E24:22_7"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_7"><span class="lab"><font color="Green" title="E48">A44</font></span></a>, <a class="ref" href="zfmodel2.html#T5" target="_self" onmouseover="rs('zfmodel2/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E25:22_7"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:22_7"><span class="lab"><font color="Green" title="E55">A62</font></span></a>, <a class="ref" href="zf_lang1.html#T75" onmouseover="rs('zf_lang1/T75')" onmouseout="rh()">ZF_LANG1:75</a></span>;<br/><a NAME="E26:22_7"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_7"><span class="lab"><font color="Green" title="E48">A44</font></span></a>, <a class="ref" href="zfmodel2.html#T5" target="_self" onmouseover="rs('zfmodel2/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E27:22_7"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:22"><span class="lab"><font color="Green" title="E45">A41</font></span></a>, <a class="txt" href="#E37:22"><span class="lab"><font color="Green" title="E40">A32</font></span></a>, <a class="txt" href="zfmodel2.html#E13"><span class="lab"><font color="Green" title="E13">Lm3</font></span></a>, <a class="ref" href="zfmodel2.html#T6" target="_self" onmouseover="rs('zfmodel2/T6')" onmouseout="rh()">Th6</a></span>;<br/><a NAME="E28:22_7"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c20">m</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span> <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:22_7"><span class="lab"><font color="Green" title="E57">A65</font></span></a>, <a class="ref" href="zf_model.html#T15" onmouseover="rs('zf_model/T15')" onmouseout="rh()">ZF_MODEL:15</a></span>;<br/><span class="kw">hence </span><a NAME="E29:22_7"/>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c19">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c23">m3</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c16">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T73" onmouseover="rs('zf_lang1/T73')" onmouseout="rh()">ZF_LANG1:73</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="E46:22"/><span class="lab"><font color="Green" title="E48">A66</font></span>: 
<font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c18">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K12" title="ZF_LANG:func.12">Ex</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K7" title="ZF_LANG:func.7">All</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c16">H</font> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">&lt;=&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K3" title="ZF_LANG:func.3">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:22"><span class="lab"><font color="Green" title="E38">A30</font></span></a>, <a class="ref" href="zfmodel2.html#T19" target="_self" onmouseover="rs('zfmodel2/T19')" onmouseout="rh()">Th19</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="c3">G</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_8"><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">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">M</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c9">G9</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">F9</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">a</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="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">M</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c9">G9</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">F9</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">a</font> )</span><br/><span class="kw">assume </span><a NAME="E1:22_8"/>
<font color="Maroon" title="c19">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">M</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c9">G9</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">F9</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">a</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">m1</font> = <font color="Maroon" title="c19">a</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</font> ;<br/><span class="kw">set </span><font color="Maroon" title="c21">m3</font> = <span class="p1">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font>;<br/><a NAME="E3:22_8"/><span class="lab"><font color="Green" title="E49">A67</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">G9</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">F9</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">G9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">F9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T15" onmouseover="rs('funct_2/T15')" onmouseout="rh()">FUNCT_2:15</a></span>;<br/><a NAME="E4:22_8"/>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c16">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:22"><span class="lab"><font color="Green" title="E38">A30</font></span></a>, <a class="txt" href="#E46:22"><span class="lab"><font color="Green" title="E48">A66</font></span></a>, <a class="ref" href="zfmodel2.html#T10" target="_self" onmouseover="rs('zfmodel2/T10')" onmouseout="rh()">Th10</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c22">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</font><span class="kw"> such that </span><br/><a NAME="E6:22_8"/><span class="lab"><font color="Green" title="E50">A68</font></span>: 
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c22">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span> <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T73" onmouseover="rs('zf_lang1/T73')" onmouseout="rh()">ZF_LANG1:73</a></span>;<br/><div><span class="lab"><font color="Green" title="E51">A69</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_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">  for <font color="Olive" title="b1">x</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c23">x</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</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="c23">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:22_8_1"/><span class="lab"><font color="Green" title="E52">A70</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</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"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font></span><br/><a NAME="E2:22_8_1"/><span class="lab"><font color="Green" title="E53">A71</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/><a NAME="E3:22_8_1"/><span class="lab"><font color="Green" title="E54">A72</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T32" onmouseover="rs('funct_7/T32')" onmouseout="rh()">FUNCT_7:32</a>, <a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a></span>;<br/><a NAME="E4:22_8_1"/><span class="lab"><font color="Green" title="E55">A73</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T32" onmouseover="rs('funct_7/T32')" onmouseout="rh()">FUNCT_7:32</a>, <a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a></span>;<br/><a NAME="E5:22_8_1"/><span class="lab"><font color="Green" title="E56">A74</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">m1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/><a NAME="E6:22_8_1"/>
( <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 or <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 or ( <font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 &amp; <font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 ) )
 ;<br/><a NAME="E7:22_8_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> or ( <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">v3</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_8_1"><span class="lab"><font color="Green" title="E53">A71</font></span></a>, <a class="txt" href="#E5:22_8_1"><span class="lab"><font color="Green" title="E56">A74</font></span></a>, <a class="txt" href="#E4:22_8_1"><span class="lab"><font color="Green" title="E55">A73</font></span></a>, <a class="txt" href="#E3:22_8_1"><span class="lab"><font color="Green" title="E54">A72</font></span></a>, <a class="ref" href="funct_7.html#T32" onmouseover="rs('funct_7/T32')" onmouseout="rh()">FUNCT_7:32</a>, <a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/><span class="kw">hence </span><a NAME="E8:22_8_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:22"><span class="lab"><font color="Green" title="E35">A16</font></span></a>, <a class="txt" href="#E1:22_8_1"><span class="lab"><font color="Green" title="E52">A70</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="E52">A75</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_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">  for <font color="Olive" title="b1">x</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c23">x</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</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="c23">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:22_8_2"/>
<font color="Maroon" title="c23">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c6">H2</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"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font></span><br/><a NAME="E2:22_8_2"/><span class="kw">then </span>
( (  not <font color="Maroon" title="c23">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c12">H3</font> &amp; <font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 &amp; <font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 ) or <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 or <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:22"><span class="lab"><font color="Green" title="E43">A35</font></span></a></span>;<br/><a NAME="E3:22_8_2"/><span class="kw">then </span>
( ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> &amp; <font color="Maroon" title="c18">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> &amp; <font color="Maroon" title="c7">v2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> ) or ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">n</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">n</font> ) or ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:22"><span class="lab"><font color="Green" title="E35">A16</font></span></a>, <a class="txt" href="zfmodel2.html#E13"><span class="lab"><font color="Green" title="E13">Lm3</font></span></a>, <a class="ref" href="funct_7.html#T32" onmouseover="rs('funct_7/T32')" onmouseout="rh()">FUNCT_7:32</a>, <a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/><span class="kw">hence </span><a NAME="E4:22_8_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c23">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"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E9:22_8"/><span class="lab"><font color="Green" title="E53">A76</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T128" onmouseover="rs('funct_7/T128')" onmouseout="rh()">FUNCT_7:128</a></span>;<br/><a NAME="E10:22_8"/>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c22">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:22_8"><span class="lab"><font color="Green" title="E50">A68</font></span></a>, <a class="ref" href="zf_model.html#T15" onmouseover="rs('zf_model/T15')" onmouseout="rh()">ZF_MODEL:15</a></span>;<br/><a NAME="E11:22_8"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:22"><span class="lab"><font color="Green" title="E42">A34</font></span></a>, <a class="txt" href="#E9:22_8"><span class="lab"><font color="Green" title="E53">A76</font></span></a>, <a class="ref" href="zfmodel2.html#T12" target="_self" onmouseover="rs('zfmodel2/T12')" onmouseout="rh()">Th12</a></span>;<br/><a NAME="E12:22_8"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmodel2.html#T8" target="_self" onmouseover="rs('zfmodel2/T8')" onmouseout="rh()">Th8</a></span>;<br/><a NAME="E13:22_8"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c22">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:22"><span class="lab"><font color="Green" title="E45">A41</font></span></a>, <a class="txt" href="#E37:22"><span class="lab"><font color="Green" title="E40">A32</font></span></a>, <a class="txt" href="zfmodel2.html#E13"><span class="lab"><font color="Green" title="E13">Lm3</font></span></a>, <a class="ref" href="zfmodel2.html#T6" target="_self" onmouseover="rs('zfmodel2/T6')" onmouseout="rh()">Th6</a></span>;<br/><a NAME="E14:22_8"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:22"><span class="lab"><font color="Green" title="E42">A34</font></span></a>, <a class="ref" href="zfmodel2.html#T5" target="_self" onmouseover="rs('zfmodel2/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E15:22_8"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">v2</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c6">H2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:22_8"><span class="lab"><font color="Green" title="E52">A75</font></span></a>, <a class="ref" href="zf_lang1.html#T75" onmouseover="rs('zf_lang1/T75')" onmouseout="rh()">ZF_LANG1:75</a></span>;<br/><a NAME="E16:22_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A77</font></span>: 
<font color="Maroon" title="c9">G9</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c22">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:22"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E8:22"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E44:22"><span class="lab"><font color="Green" title="E47">A43</font></span></a>, <a class="ref" href="zfmodel2.html#T10" target="_self" onmouseover="rs('zfmodel2/T10')" onmouseout="rh()">Th10</a></span>;<br/><a NAME="E17:22_8"/>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c22">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:22_8"><span class="lab"><font color="Green" title="E50">A68</font></span></a>, <a class="ref" href="zf_model.html#T15" onmouseover="rs('zf_model/T15')" onmouseout="rh()">ZF_MODEL:15</a></span>;<br/><a NAME="E18:22_8"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">m1</font></span>)</span>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:22"><span class="lab"><font color="Green" title="E46">A42</font></span></a>, <a class="txt" href="#E9:22_8"><span class="lab"><font color="Green" title="E53">A76</font></span></a>, <a class="ref" href="zfmodel2.html#T12" target="_self" onmouseover="rs('zfmodel2/T12')" onmouseout="rh()">Th12</a></span>;<br/><a NAME="E19:22_8"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmodel2.html#T8" target="_self" onmouseover="rs('zfmodel2/T8')" onmouseout="rh()">Th8</a></span>;<br/><a NAME="E20:22_8"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c22">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:22"><span class="lab"><font color="Green" title="E39">A31</font></span></a>, <a class="ref" href="funct_7.html#T33" onmouseover="rs('funct_7/T33')" onmouseout="rh()">FUNCT_7:33</a>, <a class="ref" href="zf_lang1.html#T76" onmouseover="rs('zf_lang1/T76')" onmouseout="rh()">ZF_LANG1:76</a></span>;<br/><a NAME="E21:22_8"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c18">v</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:22"><span class="lab"><font color="Green" title="E46">A42</font></span></a>, <a class="ref" href="zfmodel2.html#T5" target="_self" onmouseover="rs('zfmodel2/T5')" onmouseout="rh()">Th5</a></span>;<br/><a NAME="E22:22_8"/><span class="kw">then </span>
<font color="Maroon" title="c1">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c13">v3</font> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c20">m1</font>)</span>)</span> <a href="zf_lang1.html#K2" title="ZF_LANG1:func.2">/</a> (<span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c22">n</font>) <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c12">H3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:22_8"><span class="lab"><font color="Green" title="E51">A69</font></span></a>, <a class="ref" href="zf_lang1.html#T75" onmouseover="rs('zf_lang1/T75')" onmouseout="rh()">ZF_LANG1:75</a></span>;<br/><span class="kw">hence </span><a NAME="E23:22_8"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">G9</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">F9</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="txt" href="#E19:22"><span class="lab"><font color="Green" title="E30">A11</font></span></a>, <a class="txt" href="#E20:22"><span class="lab"><font color="Green" title="E31">A12</font></span></a>, <a class="txt" href="#E21:22"><span class="lab"><font color="Green" title="E32">A13</font></span></a>, <a class="txt" href="#E16:22_8"><span class="lab"><font color="Green" title="E54">A77</font></span></a>, <a class="txt" href="#E3:22_8"><span class="lab"><font color="Green" title="E49">A67</font></span></a>, <a class="ref" href="zfmodel2.html#T10" target="_self" onmouseover="rs('zfmodel2/T10')" onmouseout="rh()">Th10</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="E48:22"/>
<font color="Maroon" title="c3">G</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> (<font color="Maroon" title="c16">H</font>,<font color="Maroon" title="c18">v</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T12" onmouseover="rs('funct_2/T12')" onmouseout="rh()">FUNCT_2:12</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>
