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<span class="kw">set </span><font color="Maroon" title="c3">II</font> = <font color="Maroon" title="c2">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">AF</font> =  <a href="fomodel1.html#K32" title="FOMODEL1:func.32">AtomicFormulasOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font>,   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K32" title="FOMODEL1:func.32">AtomicFormulasOf</a> <font color="Maroon" title="c1">S</font>) <span class="kw">-&gt; </span>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  = $1 <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> $2;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel1.html#K32" title="FOMODEL1:func.32">AtomicFormulasOf</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a><span class="kw"> such that </span><br/><a NAME="E2:51_1_1"/><span class="lab"><font color="Green" title="E16">B1</font></span>: 
 for <font color="Olive" title="b1">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b2">phi</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K32" title="FOMODEL1:func.32">AtomicFormulasOf</a> <font color="Maroon" title="c1">S</font> holds  <font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">phi</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">phi</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="binop_1.html#S4" title="BINOP_1:sch.4">BINOP_1:sch 4</a>();<br/></span>
<span class="kw">take </span>
<font color="Maroon" title="c5">f</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">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b2">phi</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K32" title="FOMODEL1:func.32">AtomicFormulasOf</a> <font color="Maroon" title="c1">S</font> holds  <font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">phi</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">I</font> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Olive" title="b2">phi</font></span><br/>

<span class="kw">thus </span><a NAME="E3:51_1_1"/>
 for <font color="Olive" title="b1">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b2">phi</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K32" title="FOMODEL1:func.32">AtomicFormulasOf</a> <font color="Maroon" title="c1">S</font> holds  <font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">phi</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">I</font> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Olive" title="b2">phi</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">I</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">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">phi</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K32" title="FOMODEL1:func.32">AtomicFormulasOf</a> <font color="Maroon" title="c1">S</font> holds  <font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c6">I</font>,<font color="Olive" title="b1">phi</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Olive" title="b1">phi</font></span><br/><span class="kw">let </span><font color="Maroon" title="c7">phi</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K32" title="FOMODEL1:func.32">AtomicFormulasOf</a> <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">phi</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Maroon" title="c7">phi</font></span><br/>



<span class="kw">thus </span><a NAME="E1:51_1_1_1"/>
<font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">phi</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Maroon" title="c7">phi</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:51_1_1"><span class="lab"><font color="Green" title="E16">B1</font></span></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><span class="kw">end;</span></div>


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