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

<span class="kw">let </span><font color="Maroon" title="c1">Z</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="orders_4.html#V1" title="ORDERS_4:attr.1">countable</a>  <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b2">D</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Olive" title="b1">S</font>  st <font color="Olive" title="b2">D</font> is 2 <a href="fomodel4.html#V12" title="FOMODEL4:attr.12">-ranked</a>  &amp; <font color="Olive" title="b2">D</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Olive" title="b2">D</font> is  <a href="fomodel4.html#V16" title="FOMODEL4:attr.16">Correct</a>  &amp;  not <font color="Maroon" title="c1">Z</font> is <font color="Olive" title="b2">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  &amp; <font color="Maroon" title="c1">Z</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">S</font> holds <br/> ex <font color="Olive" title="b3">U</font> being   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>  ex <font color="Olive" title="b4">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Olive" title="b1">S</font> st <font color="Maroon" title="c1">Z</font> is <font color="Olive" title="b4">I</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="orders_4.html#V1" title="ORDERS_4:attr.1">countable</a>  <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">D</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c2">S</font>  st <font color="Olive" title="b1">D</font> is 2 <a href="fomodel4.html#V12" title="FOMODEL4:attr.12">-ranked</a>  &amp; <font color="Olive" title="b1">D</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Olive" title="b1">D</font> is  <a href="fomodel4.html#V16" title="FOMODEL4:attr.16">Correct</a>  &amp;  not <font color="Maroon" title="c1">Z</font> is <font color="Olive" title="b1">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  &amp; <font color="Maroon" title="c1">Z</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="c2">S</font> holds <br/> ex <font color="Olive" title="b2">U</font> being   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>  ex <font color="Olive" title="b3">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b2">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font> st <font color="Maroon" title="c1">Z</font> is <font color="Olive" title="b3">I</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a> </span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">S1</font> = <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">D</font> be   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c2">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="c4">D</font> is 2 <a href="fomodel4.html#V12" title="FOMODEL4:attr.12">-ranked</a>  &amp; <font color="Maroon" title="c4">D</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Maroon" title="c4">D</font> is  <a href="fomodel4.html#V16" title="FOMODEL4:attr.16">Correct</a>  &amp;  not <font color="Maroon" title="c1">Z</font> is <font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  &amp; <font color="Maroon" title="c1">Z</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="c2">S</font> implies  ex <font color="Olive" title="b1">U</font> being   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>  ex <font color="Olive" title="b2">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font> st <font color="Maroon" title="c1">Z</font> is <font color="Olive" title="b2">I</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>  )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">FF1</font> =  <a href="fomodel2.html#K33" title="FOMODEL2:func.33">AllFormulasOf</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">assume </span><a NAME="E1:261"/><span class="lab"><font color="Green" title="E140">B4</font></span>: 
( <font color="Maroon" title="c4">D</font> is 2 <a href="fomodel4.html#V12" title="FOMODEL4:attr.12">-ranked</a>  &amp; <font color="Maroon" title="c4">D</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Maroon" title="c4">D</font> is  <a href="fomodel4.html#V16" title="FOMODEL4:attr.16">Correct</a>  &amp;  not <font color="Maroon" title="c1">Z</font> is <font color="Maroon" title="c4">D</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  &amp; <font color="Maroon" title="c1">Z</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="c2">S</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">U</font> being   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>  ex <font color="Olive" title="b2">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font> st <font color="Maroon" title="c1">Z</font> is <font color="Olive" title="b2">I</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a> </span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">X</font> = <font color="Maroon" title="c1">Z</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="fomodel2.html#K33" title="FOMODEL2:func.33">AllFormulasOf</a> <font color="Maroon" title="c2">S</font></span>)</span> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">S2</font> = <font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">O1</font> =  <a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">O2</font> =  <a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">FF2</font> =  <a href="fomodel2.html#K33" title="FOMODEL2:func.33">AllFormulasOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">SS1</font> =  <a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">SS2</font> =  <a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">strings2</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">L2</font> =  <a href="fomodel1.html#K16" title="FOMODEL1:func.16">LettersOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c15">D1</font> = <font color="Maroon" title="c4">D</font> as  2 <a href="fomodel4.html#V12" title="FOMODEL4:attr.12">-ranked</a>   <a href="fomodel4.html#V16" title="FOMODEL4:attr.16">Correct</a>  <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c2">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:261"><span class="lab"><font color="Green" title="E140">B4</font></span></a></span>;<br/>
<a NAME="E4:261"/>
<span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<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="c2">S</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">D2</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span> <a href="fomodel4.html#K37" title="FOMODEL4:func.37">-rules</a>  as   <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  2 <a href="fomodel4.html#V12" title="FOMODEL4:attr.12">-ranked</a>   <a href="fomodel4.html#V16" title="FOMODEL4:attr.16">Correct</a>  <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c18">sub1</font> = <font color="Maroon" title="c6">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c6">X</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c19">sub2</font> =  <a href="fomodel0.html#K21" title="FOMODEL0:func.21">SymbolsOf</a> <font color="Maroon" title="c18">sub1</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="fomodel0.html#K21" title="FOMODEL0:func.21">SymbolsOf</a> <font color="Maroon" title="c6">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T46" title="FOMODEL0:th.46">FOMODEL0:46</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c20">inf</font> = <span class="p1">(<span class="default"><a href="fomodel1.html#K16" title="FOMODEL1:func.16">LettersOf</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="fomodel0.html#K21" title="FOMODEL0:func.21">SymbolsOf</a> <font color="Maroon" title="c6">X</font></span>)</span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel1.html#K16" title="FOMODEL1:func.16">LettersOf</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c19">sub2</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T34" title="XBOOLE_1:th.34">XBOOLE_1:34</a></span>;<br/>
<a NAME="E10:261"/><span class="lab"><font color="Green" title="E141">BB2</font></span>: 
 not <span class="p1">(<span class="default"><a href="fomodel1.html#K16" title="FOMODEL1:func.16">LettersOf</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">sub2</font> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <font color="Maroon" title="c20">inf</font></span>)</span> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="261_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c21">Y</font> be   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c6">X</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="c21">Y</font> is <font color="Maroon" title="c17">D2</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a> </span><br/><span class="kw">reconsider </span><font color="Maroon" title="c22">YY</font> = <font color="Maroon" title="c21">Y</font> as   <a href="funct_1.html#V4" title="FUNCT_1:attr.4">functional</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c23">YYY</font> = <font color="Maroon" title="c22">YY</font> as   <a href="funct_1.html#V4" title="FUNCT_1:attr.4">functional</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="fomodel2.html#K33" title="FOMODEL2:func.33">AllFormulasOf</a> <font color="Maroon" title="c2">S</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><a NAME="E3:261_1"/>
( <font color="Maroon" title="c22">YY</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &amp;  <a href="fomodel2.html#K33" title="FOMODEL2:func.33">AllFormulasOf</a> <font color="Maroon" title="c2">S</font> is  <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a>  &amp;  not <font color="Maroon" title="c22">YY</font> is <font color="Maroon" title="c15">D1</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a>  &amp; <font color="Maroon" title="c15">D1</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:261"><span class="lab"><font color="Green" title="E140">B4</font></span></a>, <a class="ref" href="fomodel4.html#T15" target="_self" title="FOMODEL4:th.15">Th16</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c24">U</font> being   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> <span class="kw"> such that </span><br/><a NAME="E5:261_1"/><span class="lab"><font color="Green" title="E142">C1</font></span>: 
 ex <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="c24">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font> st <font color="Maroon" title="c22">YY</font> is <font color="Olive" title="b1">I1</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E170"><span class="lab"><font color="Green" title="E137">Lm38</font></span></a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c25">II1</font> = <font color="Maroon" title="c24">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font>;<br/><span class="kw">set </span><font color="Maroon" title="c26">II2</font> = <font color="Maroon" title="c24">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c27">I02</font> =  the  <font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font>,<font color="Maroon" title="c24">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/><span class="kw">consider </span><font color="Maroon" title="c28">I1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c24">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font><span class="kw"> such that </span><br/><a NAME="E7:261_1"/><span class="lab"><font color="Green" title="E143">C2</font></span>: 
<font color="Maroon" title="c23">YYY</font> is <font color="Maroon" title="c28">I1</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:261_1"><span class="lab"><font color="Green" title="E142">C1</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c29">I2</font> = <span class="p1">(<span class="default"> the  <font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font>,<font color="Maroon" title="c24">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c28">I1</font></span>)</span> <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> <span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span></span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c24">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#T2" title="FOMODEL2:th.2">FOMODEL2:2</a></span>;<br/><font color="Maroon" title="c29">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="c2">S</font></span>)</span> = 
<span class="p1">(<span class="default"> the  <font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font>,<font color="Maroon" title="c24">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c28">I1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</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="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span></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/>.= 
<span class="p1">(<span class="default"> the  <font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font>,<font color="Maroon" title="c24">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c2">S</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c28">I1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c2">S</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T71" title="FUNCT_4:th.71">FUNCT_4:71</a></span>
<br/>.= 
<font color="Maroon" title="c28">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="c2">S</font></span>)</span>

;<br/><a NAME="E10:261_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">YYY</font> is <font color="Maroon" title="c29">I2</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:261_1"><span class="lab"><font color="Green" title="E143">C2</font></span></a>, <a class="txt" href="fomodel4.html#E171"><span class="lab"><font color="Green" title="E138">Lm39</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E11:261_1"/>
 not <font color="Maroon" title="c21">Y</font> is <font color="Maroon" title="c17">D2</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E139"><span class="lab"><font color="Green" title="E109">Lm11</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>
<a NAME="E12:261"/><span class="kw">then </span>
 not <font color="Maroon" title="c6">X</font> is <font color="Maroon" title="c17">D2</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-inconsistent</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E136"><span class="lab"><font color="Green" title="E106">Lm1</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c21">U</font> being   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> <span class="kw"> such that </span><br/><a NAME="E14:261"/><span class="lab"><font color="Green" title="E142">B1</font></span>: 
 ex <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="c21">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span> st <font color="Maroon" title="c6">X</font> is <font color="Olive" title="b1">I</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:261"><span class="lab"><font color="Green" title="E141">BB2</font></span></a>, <a class="txt" href="fomodel4.html#E169"><span class="lab"><font color="Green" title="E136">Lm37</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c22">II1</font> = <font color="Maroon" title="c21">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c23">II2</font> = <font color="Maroon" title="c21">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c24">I2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c21">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel1.html#K41" title="FOMODEL1:func.41">addLettersNotIn</a> <font color="Maroon" title="c6">X</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E16:261"/><span class="lab"><font color="Green" title="E143">B3</font></span>: 
<font color="Maroon" title="c6">X</font> is <font color="Maroon" title="c24">I2</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:261"><span class="lab"><font color="Green" title="E142">B1</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c21">U</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <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="c21">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font> st <font color="Maroon" title="c1">Z</font> is <font color="Olive" title="b1">I</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a> </span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c25">I1</font> = <font color="Maroon" title="c24">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="c2">S</font></span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c21">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#T2" title="FOMODEL2:th.2">FOMODEL2:2</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c25">I1</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="c1">Z</font> is <font color="Maroon" title="c25">I1</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a> </span><br/>

<a NAME="E18:261"/>
<font color="Maroon" title="c25">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="c2">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">I2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c2">S</font></span>)</span></span>)</span> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c2">S</font></span>)</span>
 
;<br/>
<span class="kw">hence </span><a NAME="E19:261"/>
<font color="Maroon" title="c1">Z</font> is <font color="Maroon" title="c25">I1</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:261"><span class="lab"><font color="Green" title="E143">B3</font></span></a>, <a class="txt" href="fomodel4.html#E171"><span class="lab"><font color="Green" title="E138">Lm39</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>
