<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">U</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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">X</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/>  for <font color="Olive" title="b2">S1</font>, <font color="Olive" title="b3">S2</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b4">I1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Olive" title="b2">S1</font><br/>  for <font color="Olive" title="b5">I2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Olive" title="b3">S2</font>  st <font color="Olive" title="b3">S2</font> is <font color="Olive" title="b2">S1</font> <a href="fomodel1.html#V16" title="FOMODEL1:attr.16">-extending</a>  &amp; <font color="Olive" title="b1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="fomodel2.html#K33" title="FOMODEL2:func.33">AllFormulasOf</a> <font color="Olive" title="b2">S1</font> &amp; <font color="Olive" title="b4">I1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Olive" title="b2">S1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">I2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Olive" title="b2">S1</font></span>)</span> holds <br/>( <font color="Olive" title="b1">X</font> is <font color="Olive" title="b4">I1</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>  iff <font color="Olive" title="b1">X</font> is <font color="Olive" title="b5">I2</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">X</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">S1</font>, <font color="Olive" title="b2">S2</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b3">I1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Olive" title="b1">S1</font><br/>  for <font color="Olive" title="b4">I2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Olive" title="b2">S2</font>  st <font color="Olive" title="b2">S2</font> is <font color="Olive" title="b1">S1</font> <a href="fomodel1.html#V16" title="FOMODEL1:attr.16">-extending</a>  &amp; <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="fomodel2.html#K33" title="FOMODEL2:func.33">AllFormulasOf</a> <font color="Olive" title="b1">S1</font> &amp; <font color="Olive" title="b3">I1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Olive" title="b1">S1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">I2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Olive" title="b1">S1</font></span>)</span> holds <br/>( <font color="Maroon" title="c2">X</font> is <font color="Olive" title="b3">I1</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>  iff <font color="Maroon" title="c2">X</font> is <font color="Olive" title="b4">I2</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">S1</font>, <font color="Maroon" title="c4">S2</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">I1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c3">S1</font><br/>  for <font color="Olive" title="b2">I2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c4">S2</font>  st <font color="Maroon" title="c4">S2</font> is <font color="Maroon" title="c3">S1</font> <a href="fomodel1.html#V16" title="FOMODEL1:attr.16">-extending</a>  &amp; <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="fomodel2.html#K33" title="FOMODEL2:func.33">AllFormulasOf</a> <font color="Maroon" title="c3">S1</font> &amp; <font color="Olive" title="b1">I1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c3">S1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">I2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c3">S1</font></span>)</span> holds <br/>( <font color="Maroon" title="c2">X</font> is <font color="Olive" title="b1">I1</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>  iff <font color="Maroon" title="c2">X</font> is <font color="Olive" title="b2">I2</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>  )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">II1</font> = <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c3">S1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">II2</font> = <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c4">S2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">a1</font> =  the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c3">S1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">a2</font> =  the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c4">S2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">O1</font> =  <a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c3">S1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">E1</font> =  <a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c3">S1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">E2</font> =  <a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c4">S2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">N1</font> =  <a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c3">S1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">N2</font> =  <a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c4">S2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">FF1</font> =  <a href="fomodel2.html#K33" title="FOMODEL2:func.33">AllFormulasOf</a> <font color="Maroon" title="c3">S1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">AS1</font> =  <a href="fomodel1.html#K17" title="FOMODEL1:func.17">AtomicFormulaSymbolsOf</a> <font color="Maroon" title="c3">S1</font>;<br/>
<a NAME="E1:254"/>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c3">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel1.html#K17" title="FOMODEL1:func.17">AtomicFormulaSymbolsOf</a> <font color="Maroon" title="c3">S1</font> &amp;  <a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c3">S1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="fomodel1.html#K17" title="FOMODEL1:func.17">AtomicFormulaSymbolsOf</a> <font color="Maroon" title="c3">S1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#T1" title="FOMODEL1:th.1">FOMODEL1:1</a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c16">O11</font> =  <a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c3">S1</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c3">S1</font></span>)</span> ;<br/>
<span class="kw">let </span><font color="Maroon" title="c17">I1</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c3">S1</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">I2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c4">S2</font>  st <font color="Maroon" title="c4">S2</font> is <font color="Maroon" title="c3">S1</font> <a href="fomodel1.html#V16" title="FOMODEL1:attr.16">-extending</a>  &amp; <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="fomodel2.html#K33" title="FOMODEL2:func.33">AllFormulasOf</a> <font color="Maroon" title="c3">S1</font> &amp; <font color="Maroon" title="c17">I1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c3">S1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">I2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c3">S1</font></span>)</span> holds <br/>( <font color="Maroon" title="c2">X</font> is <font color="Maroon" title="c17">I1</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>  iff <font color="Maroon" title="c2">X</font> is <font color="Olive" title="b1">I2</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c18">I2</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c4">S2</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="c4">S2</font> is <font color="Maroon" title="c3">S1</font> <a href="fomodel1.html#V16" title="FOMODEL1:attr.16">-extending</a>  &amp; <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="fomodel2.html#K33" title="FOMODEL2:func.33">AllFormulasOf</a> <font color="Maroon" title="c3">S1</font> &amp; <font color="Maroon" title="c17">I1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c3">S1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">I2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c3">S1</font></span>)</span> implies ( <font color="Maroon" title="c2">X</font> is <font color="Maroon" title="c17">I1</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>  iff <font color="Maroon" title="c2">X</font> is <font color="Maroon" title="c18">I2</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>  ) )</span><br/>



<span class="kw">assume </span><a NAME="E3:254"/><span class="lab"><font color="Green" title="E139">B5</font></span>: 
<font color="Maroon" title="c4">S2</font> is <font color="Maroon" title="c3">S1</font> <a href="fomodel1.html#V16" title="FOMODEL1:attr.16">-extending</a> 
 ; <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="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="fomodel2.html#K33" title="FOMODEL2:func.33">AllFormulasOf</a> <font color="Maroon" title="c3">S1</font> or  not <font color="Maroon" title="c17">I1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c3">S1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">I2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c3">S1</font></span>)</span> or ( <font color="Maroon" title="c2">X</font> is <font color="Maroon" title="c17">I1</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>  iff <font color="Maroon" title="c2">X</font> is <font color="Maroon" title="c18">I2</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>  ) )</span><br/>

<a NAME="E4:254"/><span class="kw">then </span>
 the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c3">S1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c4">S2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D41" title="FOMODEL1:def.41">FOMODEL1:def 41</a></span>;<br/>
<span class="kw">then </span> the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c3">S1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c3">S1</font></span>)</span> = 
<span class="p1">(<span class="default"> the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c4">S2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c3">S1</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c3">S1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="grfunc_1.html#T23" title="GRFUNC_1:th.23">GRFUNC_1:23</a></span>
<br/>.= 
 the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c4">S2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">O11</font> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c3">S1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></span>
;<br/>
<a NAME="E6:254"/><span class="kw">then </span><span class="lab"><font color="Green" title="E140">B1</font></span>: 
(  the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c3">S1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c3">S1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c4">S2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c3">S1</font></span>)</span> &amp;  <a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c3">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c4">S2</font> &amp;  <a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c3">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c4">S2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:254"><span class="lab"><font color="Green" title="E139">B5</font></span></a>, <a class="ref" href="fomodel1.html#D41" title="FOMODEL1:def.41">FOMODEL1:def 41</a></span>;<br/>
<span class="kw">assume </span><a NAME="E7:254"/><span class="lab"><font color="Green" title="E141">B2</font></span>: 
( <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="fomodel2.html#K33" title="FOMODEL2:func.33">AllFormulasOf</a> <font color="Maroon" title="c3">S1</font> &amp; <font color="Maroon" title="c17">I1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c3">S1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">I2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c3">S1</font></span>)</span> )
 ; <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="c2">X</font> is <font color="Maroon" title="c17">I1</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>  iff <font color="Maroon" title="c2">X</font> is <font color="Maroon" title="c18">I2</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>  )</span><br/>

<div><span class="kw">hereby </span> <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="c2">X</font> is <font color="Maroon" title="c18">I2</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>  implies <font color="Maroon" title="c2">X</font> is <font color="Maroon" title="c17">I1</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>  )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:254_2"/><span class="lab"><font color="Green" title="E142">B3</font></span>: 
<font color="Maroon" title="c2">X</font> is <font color="Maroon" title="c17">I1</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a> 
 ; <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="c2">X</font> is <font color="Maroon" title="c18">I2</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a> </span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="254_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">phi2</font> be   <a href="fomodel2.html#V4" title="FOMODEL2:attr.4">wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c4">S2</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="c19">phi2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> implies <font color="Maroon" title="c18">I2</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c19">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/><span class="kw">assume </span><a NAME="E1:254_2_1"/><span class="lab"><font color="Green" title="E143">C0</font></span>: 
<font color="Maroon" title="c19">phi2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</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="c18">I2</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c19">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><a NAME="E2:254_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">phi2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fomodel2.html#K33" title="FOMODEL2:func.33">AllFormulasOf</a> <font color="Maroon" title="c3">S1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:254"><span class="lab"><font color="Green" title="E141">B2</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">phi1</font> = <font color="Maroon" title="c19">phi2</font> as   <a href="fomodel2.html#V4" title="FOMODEL2:attr.4">wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c3">S1</font> ;<br/><span class="kw">consider </span><font color="Maroon" title="c21">phi22</font> being   <a href="fomodel2.html#V4" title="FOMODEL2:attr.4">wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c4">S2</font><span class="kw"> such that </span><br/><a NAME="E5:254_2_1"/><span class="lab"><font color="Green" title="E144">C1</font></span>: 
( <font color="Maroon" title="c20">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">phi22</font> &amp; <font color="Maroon" title="c17">I1</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c20">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">I2</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c21">phi22</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:254"><span class="lab"><font color="Green" title="E140">B1</font></span></a>, <a class="txt" href="#E7:254"><span class="lab"><font color="Green" title="E141">B2</font></span></a>, <a class="ref" href="fomodel3.html#T12" title="FOMODEL3:th.12">FOMODEL3:12</a></span>;<br/><span class="kw">thus </span><a NAME="E6:254_2_1"/>
<font color="Maroon" title="c18">I2</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c19">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:254_2_1"><span class="lab"><font color="Green" title="E144">C1</font></span></a>, <a class="txt" href="#E1:254_2_1"><span class="lab"><font color="Green" title="E143">C0</font></span></a>, <a class="txt" href="#E1:254_2"><span class="lab"><font color="Green" title="E142">B3</font></span></a>, <a class="ref" href="fomodel2.html#D42" title="FOMODEL2:def.42">FOMODEL2:def 42</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><span class="kw">hence </span><a NAME="E3:254_2"/>
<font color="Maroon" title="c2">X</font> is <font color="Maroon" title="c18">I2</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D42" title="FOMODEL2:def.42">FOMODEL2:def 42</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>

<span class="kw">assume </span><a NAME="E9:254"/><span class="lab"><font color="Green" title="E142">B4</font></span>: 
<font color="Maroon" title="c2">X</font> is <font color="Maroon" title="c18">I2</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a> 
 ; <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="c2">X</font> is <font color="Maroon" title="c17">I1</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="254_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">phi1</font> be   <a href="fomodel2.html#V4" title="FOMODEL2:attr.4">wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c3">S1</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="c19">phi1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> implies <font color="Maroon" title="c17">I1</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c19">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/><span class="kw">assume </span><a NAME="E1:254_3"/><span class="lab"><font color="Green" title="E143">C0</font></span>: 
<font color="Maroon" title="c19">phi1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</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="c17">I1</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c19">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><span class="kw">consider </span><font color="Maroon" title="c20">phi2</font> being   <a href="fomodel2.html#V4" title="FOMODEL2:attr.4">wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c4">S2</font><span class="kw"> such that </span><br/><a NAME="E3:254_3"/><span class="lab"><font color="Green" title="E144">C1</font></span>: 
( <font color="Maroon" title="c19">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">phi2</font> &amp; <font color="Maroon" title="c17">I1</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c19">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">I2</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c20">phi2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:254"><span class="lab"><font color="Green" title="E140">B1</font></span></a>, <a class="txt" href="#E7:254"><span class="lab"><font color="Green" title="E141">B2</font></span></a>, <a class="ref" href="fomodel3.html#T12" title="FOMODEL3:th.12">FOMODEL3:12</a></span>;<br/><span class="kw">thus </span><a NAME="E4:254_3"/>
<font color="Maroon" title="c17">I1</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c19">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:254_3"><span class="lab"><font color="Green" title="E144">C1</font></span></a>, <a class="txt" href="#E1:254_3"><span class="lab"><font color="Green" title="E143">C0</font></span></a>, <a class="txt" href="#E9:254"><span class="lab"><font color="Green" title="E142">B4</font></span></a>, <a class="ref" href="fomodel2.html#D42" title="FOMODEL2:def.42">FOMODEL2:def 42</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>
<span class="kw">hence </span><a NAME="E11:254"/>
<font color="Maroon" title="c2">X</font> is <font color="Maroon" title="c17">I1</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D42" title="FOMODEL2:def.42">FOMODEL2:def 42</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>
