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<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b2">r</font> being   <a href="fomodel1.html#V7" title="FOMODEL1:attr.7">relational</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">D</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Olive" title="b1">S</font>  st <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Olive" title="b1">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">D</font> &amp; <font color="Maroon" title="c1">X</font> is <font color="Olive" title="b3">D</font> <a href="fomodel4.html#V10" title="FOMODEL4:attr.10">-expanded</a>  &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Olive" title="b2">r</font></span>)</span></span>)</span> <a href="fomodel3.html#K9" title="FOMODEL3:func.9">-placesOf</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b3">D</font>) <a href="fomodel4.html#K6" title="FOMODEL4:func.6">-termEq</a></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b2">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">S</font> be   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">r</font> being   <a href="fomodel1.html#V7" title="FOMODEL1:attr.7">relational</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Maroon" title="c4">S</font><br/>  for <font color="Olive" title="b2">D</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c4">S</font>  st <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c4">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">D</font> &amp; <font color="Maroon" title="c1">X</font> is <font color="Olive" title="b2">D</font> <a href="fomodel4.html#V10" title="FOMODEL4:attr.10">-expanded</a>  &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Olive" title="b1">r</font></span>)</span></span>)</span> <a href="fomodel3.html#K9" title="FOMODEL3:func.9">-placesOf</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b2">D</font>) <a href="fomodel4.html#K6" title="FOMODEL4:func.6">-termEq</a></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">r</font> be   <a href="fomodel1.html#V7" title="FOMODEL1:attr.7">relational</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Maroon" title="c4">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">D</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c4">S</font>  st <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c4">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">D</font> &amp; <font color="Maroon" title="c1">X</font> is <font color="Olive" title="b1">D</font> <a href="fomodel4.html#V10" title="FOMODEL4:attr.10">-expanded</a>  &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c5">r</font></span>)</span></span>)</span> <a href="fomodel3.html#K9" title="FOMODEL3:func.9">-placesOf</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">D</font>) <a href="fomodel4.html#K6" title="FOMODEL4:func.6">-termEq</a></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">D</font> be   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c4">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c4">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">D</font> &amp; <font color="Maroon" title="c1">X</font> is <font color="Maroon" title="c6">D</font> <a href="fomodel4.html#V10" title="FOMODEL4:attr.10">-expanded</a>  &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c5">r</font></span>)</span></span>)</span> <a href="fomodel3.html#K9" title="FOMODEL3:func.9">-placesOf</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c6">D</font>) <a href="fomodel4.html#K6" title="FOMODEL4:func.6">-termEq</a></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> )</span><br/>











<span class="kw">set </span><font color="Maroon" title="c7">s</font> = <font color="Maroon" title="c5">r</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">n</font> =  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c5">r</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">AT</font> =  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">E</font> =  <a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c4">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">Phi</font> = <font color="Maroon" title="c1">X</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">f</font> = <font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">R</font> = (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c6">D</font>) <a href="fomodel4.html#K6" title="FOMODEL4:func.6">-termEq</a> ;<br/>
<span class="kw">assume </span><a NAME="E1:107"/><span class="lab"><font color="Green" title="E78">B1</font></span>: 
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c4">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">D</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c1">X</font> is <font color="Maroon" title="c6">D</font> <a href="fomodel4.html#V10" title="FOMODEL4:attr.10">-expanded</a>  or  not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c5">r</font></span>)</span></span>)</span> <a href="fomodel3.html#K9" title="FOMODEL3:func.9">-placesOf</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c6">D</font>) <a href="fomodel4.html#K6" title="FOMODEL4:func.6">-termEq</a></span>)</span> or  not <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> or <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:107"/><span class="lab"><font color="Green" title="E79">B2</font></span>: 
<font color="Maroon" title="c1">X</font> is <font color="Maroon" title="c6">D</font> <a href="fomodel4.html#V10" title="FOMODEL4:attr.10">-expanded</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c5">r</font></span>)</span></span>)</span> <a href="fomodel3.html#K9" title="FOMODEL3:func.9">-placesOf</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c6">D</font>) <a href="fomodel4.html#K6" title="FOMODEL4:func.6">-termEq</a></span>)</span> or  not <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> or <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> )</span><br/>

<span class="kw">assume </span><a NAME="E3:107"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c5">r</font></span>)</span></span>)</span> <a href="fomodel3.html#K9" title="FOMODEL3:func.9">-placesOf</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c6">D</font>) <a href="fomodel4.html#K6" title="FOMODEL4:func.6">-termEq</a></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> or <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">T1</font>, <font color="Maroon" title="c15">T2</font> being   <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c5">r</font></span>)</span> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a> <span class="kw"> such that </span><br/><a NAME="E5:107"/><span class="lab"><font color="Green" title="E80">B0</font></span>: 
( <font color="Maroon" title="c14">T1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x1</font> &amp; <font color="Maroon" title="c15">T2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> &amp;  <a href="fomodel4.html#K36" title="FOMODEL4:func.36">PairWiseEq</a> (<font color="Maroon" title="c14">T1</font>,<font color="Maroon" title="c15">T2</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E94"><span class="lab"><font color="Green" title="E75">Lm42</font></span></a>, <a class="txt" href="#E2:107"><span class="lab"><font color="Green" title="E79">B2</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">Z</font> =  <a href="fomodel4.html#K36" title="FOMODEL4:func.36">PairWiseEq</a> (<font color="Maroon" title="c14">T1</font>,<font color="Maroon" title="c15">T2</font>);<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">w1</font> = <font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K1" title="FOMODEL3:func.1">-compound</a> <font color="Maroon" title="c14">T1</font>, <font color="Maroon" title="c18">w2</font> = <font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K1" title="FOMODEL3:func.1">-compound</a> <font color="Maroon" title="c15">T2</font> as   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c4">S</font> ;<br/>
<a NAME="E7:107"/><span class="lab"><font color="Green" title="E81">B4</font></span>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">w1</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">w2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:107"><span class="lab"><font color="Green" title="E80">B0</font></span></a>, <a class="ref" href="fomodel3.html#D2" title="FOMODEL3:def.2">FOMODEL3:def 2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E8:107"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" 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="c5">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c19">X1</font> = <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c17">w1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:107"><span class="lab"><font color="Green" title="E81">B4</font></span></a>, <a class="ref" href="zfmisc_1.html#T31" title="ZFMISC_1:th.31">ZFMISC_1:31</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c20">ZZ</font> =  <a href="fomodel4.html#K36" title="FOMODEL4:func.36">PairWiseEq</a> (<font color="Maroon" title="c14">T1</font>,<font color="Maroon" title="c15">T2</font>) as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:107"><span class="lab"><font color="Green" title="E80">B0</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c21">ZZZ</font> = <font color="Maroon" title="c20">ZZ</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c19">X1</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> ;<br/>
<a NAME="E12:107"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="fomodel4.html#K36" title="FOMODEL4:func.36">PairWiseEq</a> (<font color="Maroon" title="c14">T1</font>,<font color="Maroon" title="c15">T2</font>)</span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K1" title="FOMODEL3:func.1">-compound</a> <font color="Maroon" title="c14">T1</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K1" title="FOMODEL3:func.1">-compound</a> <font color="Maroon" title="c15">T2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c4">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="fomodel4.html#V3" title="FOMODEL4:attr.3">-derivable</a> 
 
;<br/>
<a NAME="E13:107"/><span class="kw">then </span>
<span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c21">ZZZ</font>,<font color="Maroon" title="c18">w2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="lang1.html#K4" title="LANG1:func.4">}</a></span> is  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c6">D</font> <a href="fomodel4.html#V3" title="FOMODEL4:attr.3">-derivable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E35"><span class="lab"><font color="Green" title="E30">Lm20</font></span></a>, <a class="txt" href="#E1:107"><span class="lab"><font color="Green" title="E78">B1</font></span></a></span>;<br/>
<a NAME="E14:107"/><span class="kw">then </span>
<font color="Maroon" title="c18">w2</font> is <font color="Maroon" title="c21">ZZZ</font>,<font color="Maroon" title="c6">D</font> <a href="fomodel4.html#V8" title="FOMODEL4:attr.8">-provable</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D12" target="_self" title="FOMODEL4:def.12">DefProvable</a></span>;<br/>
<a NAME="E15:107"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c18">w2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:107"><span class="lab"><font color="Green" title="E79">B2</font></span></a>, <a class="ref" href="fomodel4.html#D16" target="_self" title="FOMODEL4:def.16">DefExpanded</a></span>;<br/>
<span class="kw">hence </span><a NAME="E16:107"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:107"><span class="lab"><font color="Green" title="E81">B4</font></span></a>, <a class="ref" href="zfmisc_1.html#T31" title="ZFMISC_1:th.31">ZFMISC_1:31</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
