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<span class="kw">let </span><font color="Maroon" title="c1">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">  <a href="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c1">S</font> is  <a href="fomodel4.html#V17" title="FOMODEL4:attr.17">Correct</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="213_1"><span class="kw">now </span></a><div class="add"><span class="kw">set </span><font color="Maroon" title="c2">f</font> =  <a href="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c1">S</font>;<br/><span class="kw">set </span><font color="Maroon" title="c3">R</font> =  <a href="fomodel4.html#K14" title="FOMODEL4:func.14">P3e</a> <font color="Maroon" title="c1">S</font>;<br/><span class="kw">set </span><font color="Maroon" title="c4">Q</font> = <font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a> ;<br/><span class="kw">set </span><font color="Maroon" title="c5">E</font> =  <a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font>;<br/><span class="kw">set </span><font color="Maroon" title="c6">N</font> =  <a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c1">S</font>;<br/><span class="kw">set </span><font color="Maroon" title="c7">FF</font> =  <a href="fomodel2.html#K33" title="FOMODEL2:func.33">AllFormulasOf</a> <font color="Maroon" title="c1">S</font>;<br/><span class="kw">set </span><font color="Maroon" title="c8">TT</font> =  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c1">S</font>;<br/><span class="kw">set </span><font color="Maroon" title="c9">SS</font> =  <a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c1">S</font>;<br/><span class="kw">set </span><font color="Maroon" title="c10">F</font> = <font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a> ;<br/><span class="kw">set </span><font color="Maroon" title="c11">C</font> = <font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K21" title="FOMODEL1:func.21">-multiCat</a> ;<br/><span class="kw">let </span><font color="Maroon" title="c12">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"> ( <font color="Maroon" title="c12">X</font> is <font color="Maroon" title="c1">S</font> <a href="fomodel2.html#V12" title="FOMODEL2:attr.12">-correct</a>  implies <span class="p1">(<span class="default"><a href="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">X</font> is <font color="Maroon" title="c1">S</font> <a href="fomodel2.html#V12" title="FOMODEL2:attr.12">-correct</a>  )</span><br/><span class="kw">assume </span><a NAME="E1:213_1"/><span class="lab"><font color="Green" title="E119">B0</font></span>: 
<font color="Maroon" title="c12">X</font> is <font color="Maroon" title="c1">S</font> <a href="fomodel2.html#V12" title="FOMODEL2:attr.12">-correct</a> 
 ; <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"><a href="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">X</font> is <font color="Maroon" title="c1">S</font> <a href="fomodel2.html#V12" title="FOMODEL2:attr.12">-correct</a> </span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="213_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c13">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">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c13">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">x</font> being  <font color="Olive">b<sub>1</sub></font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/>  for <font color="Olive" title="b3">psi</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="c1">S</font>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">psi</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="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">X</font> holds <br/><font color="Olive">b<sub>5</sub></font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive">b<sub>7</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><span class="kw">set </span><font color="Maroon" title="c14">II</font> = <font color="Maroon" title="c13">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font>;<br/><span class="kw">let </span><font color="Maroon" title="c15">I</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c13">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">x</font> being  <font color="Maroon" title="c15">I</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/>  for <font color="Olive" title="b2">psi</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="c1">S</font>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">psi</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="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">X</font> holds <br/><font color="Olive">b<sub>4</sub></font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive">b<sub>6</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><span class="kw">let </span><font color="Maroon" title="c16">x</font> be  <font color="Maroon" title="c15">I</font> <a href="fomodel2.html#V10" title="FOMODEL2:attr.10">-satisfied</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">psi</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="c1">S</font>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">x</font>,<font color="Olive" title="b1">psi</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="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">X</font> holds <br/><font color="Olive">b<sub>3</sub></font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><span class="kw">let </span><font color="Maroon" title="c17">psi</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="c1">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="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">x</font>,<font color="Maroon" title="c17">psi</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="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">X</font> implies <font color="Olive">b<sub>2</sub></font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/><span class="kw">set </span><font color="Maroon" title="c18">s</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">x</font>,<font color="Maroon" title="c17">psi</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c19">TE</font> = <font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a> ;<br/><span class="kw">set </span><font color="Maroon" title="c20">d</font> = <font color="Maroon" title="c13">U</font> <a href="fomodel2.html#K2" title="FOMODEL2:func.2">-deltaInterpreter</a> ;<br/><a NAME="E1:213_1_1"/><span class="lab"><font color="Green" title="E120">CC0</font></span>: 
( <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">x</font>,<font color="Maroon" title="c17">psi</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">x</font>,<font color="Maroon" title="c17">psi</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <font color="Maroon" title="c17">psi</font> <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">assume </span><a NAME="E2:213_1_1"/><span class="lab"><font color="Green" title="E121">DD1</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">x</font>,<font color="Maroon" title="c17">psi</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="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">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="Olive">b<sub>2</sub></font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><a NAME="E3:213_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E122">D1</font></span>: 
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">x</font>,<font color="Maroon" title="c17">psi</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a>  &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c12">X</font>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">x</font>,<font color="Maroon" title="c17">psi</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fomodel4.html#K14" title="FOMODEL4:func.14">P3e</a> <font color="Maroon" title="c1">S</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E73"><span class="lab"><font color="Green" title="E68">Lm1e</font></span></a></span>;<br/><a NAME="E4:213_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="fomodel4.html#K14" title="FOMODEL4:func.14">P3e</a> <font color="Maroon" title="c1">S</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D4" title="RELAT_1:def.4">RELAT_1:def 4</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c21">Seqts</font> = <font color="Maroon" title="c12">X</font> as  <font color="Maroon" title="c1">S</font> <a href="fomodel2.html#V12" title="FOMODEL2:attr.12">-correct</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:213_1"><span class="lab"><font color="Green" title="E119">B0</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c22">seqt</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c16">x</font>,<font color="Maroon" title="c17">psi</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:213_1_1"><span class="lab"><font color="Green" title="E121">DD1</font></span></a>, <a class="txt" href="fomodel4.html#E73"><span class="lab"><font color="Green" title="E68">Lm1e</font></span></a></span>;<br/><a NAME="E7:213_1_1"/>
<font color="Maroon" title="c22">seqt</font> <a href="fomodel4.html#R7" title="FOMODEL4:pred.7">Rule3e</a> <font color="Maroon" title="c21">Seqts</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:213_1_1"><span class="lab"><font color="Green" title="E122">D1</font></span></a>, <a class="ref" href="fomodel4.html#D37" target="_self" title="FOMODEL4:def.37">DefP3e</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c23">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="c1">S</font>, <font color="Maroon" title="c24">T1</font>, <font color="Maroon" title="c25">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="c23">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="c1">S</font></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a> <span class="kw"> such that </span><br/><a NAME="E9:213_1_1"/><span class="lab"><font color="Green" title="E123">D2</font></span>: 
( <font color="Maroon" title="c22">seqt</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.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"><font color="Maroon" title="c23">r</font> <a href="fomodel3.html#K1" title="FOMODEL3:func.1">-compound</a> <font color="Maroon" title="c24">T1</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <span class="p4">(<span class="default"><font color="Olive" title="b2">TT1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">j</font></span>)</span></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">TT2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">j</font></span>)</span></span>)</span> where <font color="Olive" title="b1">j</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</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="c23">r</font></span>)</span></span>)</span>, <font color="Olive" title="b2">TT1</font>, <font color="Olive" title="b3">TT2</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c23">r</font></span>)</span></span>)</span></span>)</span>,<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> <font color="Maroon" title="c1">S</font></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> : ( <font color="Olive" title="b2">TT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">T1</font> &amp; <font color="Olive" title="b3">TT2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">T2</font> ) </span> } </span>  &amp; <font color="Maroon" title="c22">seqt</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">r</font> <a href="fomodel3.html#K1" title="FOMODEL3:func.1">-compound</a> <font color="Maroon" title="c25">T2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D24" target="_self" title="FOMODEL4:def.24">Def3e</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c26">psi0</font> = <font color="Maroon" title="c17">psi</font> as   <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c1">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:213_1_1"><span class="lab"><font color="Green" title="E120">CC0</font></span></a>, <a class="txt" href="#E9:213_1_1"><span class="lab"><font color="Green" title="E123">D2</font></span></a>, <a class="ref" href="fomodel0.html#T29" title="FOMODEL0:th.29">FOMODEL0:29</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c27">phi1</font> = <font color="Maroon" title="c23">r</font> <a href="fomodel3.html#K1" title="FOMODEL3:func.1">-compound</a> <font color="Maroon" title="c24">T1</font> as   <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c1">S</font> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c28">rr</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c26">psi0</font> as   <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="c1">S</font> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c29">Fam</font> = <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p5">(<span class="default"><a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <span class="p4">(<span class="default"><font color="Olive" title="b2">TT1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">j</font></span>)</span></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">TT2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">j</font></span>)</span></span>)</span> where <font color="Olive" title="b1">j</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</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="c23">r</font></span>)</span></span>)</span>, <font color="Olive" title="b2">TT1</font>, <font color="Olive" title="b3">TT2</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c23">r</font></span>)</span></span>)</span></span>)</span>,<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> <font color="Maroon" title="c1">S</font></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> : ( <font color="Olive" title="b2">TT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">T1</font> &amp; <font color="Olive" title="b3">TT2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">T2</font> ) </span> } </span>  <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">phi1</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="c16">x</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:213_1_1"><span class="lab"><font color="Green" title="E123">D2</font></span></a>, <a class="txt" href="#E1:213_1_1"><span class="lab"><font color="Green" title="E120">CC0</font></span></a>, <a class="ref" href="fomodel0.html#T29" title="FOMODEL0:th.29">FOMODEL0:29</a></span>;<br/><a NAME="E14:213_1_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><font color="Maroon" title="c23">r</font></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K21" title="FOMODEL1:func.21">-multiCat</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">T1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <font color="Maroon" title="c23">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><font color="Maroon" title="c23">r</font></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K21" title="FOMODEL1:func.21">-multiCat</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">T2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <font color="Maroon" title="c23">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ;<br/><a NAME="E15:213_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><span class="p2"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><font color="Maroon" title="c23">r</font></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K21" title="FOMODEL1:func.21">-multiCat</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">T1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">r</font> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><font color="Maroon" title="c23">r</font></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K21" title="FOMODEL1:func.21">-multiCat</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">T2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">r</font> &amp; <font color="Maroon" title="c26">psi0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><font color="Maroon" title="c23">r</font></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K21" title="FOMODEL1:func.21">-multiCat</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">T2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:213_1_1"><span class="lab"><font color="Green" title="E123">D2</font></span></a>, <a class="txt" href="#E1:213_1_1"><span class="lab"><font color="Green" title="E120">CC0</font></span></a>, <a class="ref" href="fomodel0.html#T29" title="FOMODEL0:th.29">FOMODEL0:29</a></span>;<br/><a NAME="E16:213_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E124">D3</font></span>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c27">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">r</font> &amp; <font color="Maroon" title="c28">rr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">r</font> &amp; <font color="Maroon" title="c26">psi0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><font color="Maroon" title="c23">r</font></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K21" title="FOMODEL1:func.21">-multiCat</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">T2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T6" title="FOMODEL0:th.6">FOMODEL0:6</a></span>;<br/><a NAME="E17:213_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E125">D4</font></span>: 
( <font color="Maroon" title="c24">T1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c27">phi1</font> &amp; <font color="Maroon" title="c25">T2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c26">psi0</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D38" title="FOMODEL1:def.38">FOMODEL1:def 38</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c30">y</font> = <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">phi1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <font color="Maroon" title="c29">Fam</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c16">x</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:213_1_1"><span class="lab"><font color="Green" title="E123">D2</font></span></a>, <a class="txt" href="#E1:213_1_1"><span class="lab"><font color="Green" title="E120">CC0</font></span></a>, <a class="ref" href="fomodel0.html#T29" title="FOMODEL0:th.29">FOMODEL0:29</a></span>;<br/><a NAME="E19:213_1_1"/><span class="lab"><font color="Green" title="E126">DD6</font></span>: 
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">phi1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c30">y</font>
 ;<br/><div><span class="lab"><font color="Green" title="E127">DD5</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="213_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">set </span><font color="Maroon" title="c31">p</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c24">T1</font>;<br/><span class="kw">set </span><font color="Maroon" title="c32">q</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c25">T2</font>;<br/><a NAME="E1:213_1_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c24">T1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c23">r</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>;<br/><span class="kw">hence </span><a NAME="E2:213_1_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c25">T2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c24">T1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>; <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">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c24">T1</font></span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c24">T1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c25">T2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font></span><br/><span class="kw">let </span><font color="Maroon" title="c33">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c33">k</font> &amp; <font color="Maroon" title="c33">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c24">T1</font></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c24">T1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c33">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c25">T2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c33">k</font> )</span><br/><span class="kw">assume </span><a NAME="E3:213_1_1_1"/><span class="lab"><font color="Green" title="E128">EE0</font></span>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c33">k</font> &amp; <font color="Maroon" title="c33">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c24">T1</font></span>)</span> )
 ; <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"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c24">T1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c33">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c25">T2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c33">k</font></span><br/><a NAME="E4:213_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E129">E0</font></span>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c33">k</font> &amp; <font color="Maroon" title="c33">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <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="c23">r</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c34">kk</font> = <font color="Maroon" title="c33">k</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</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="c23">r</font></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/><a NAME="E6:213_1_1_1"/>
<font color="Maroon" title="c33">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c33">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</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="c23">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c33">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:213_1_1_1"><span class="lab"><font color="Green" title="E129">E0</font></span></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c35">h</font> = <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="c23">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c33">k</font> as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c36">k1</font> = <font color="Maroon" title="c33">k</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">zero</a>  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:213_1_1_1"><span class="lab"><font color="Green" title="E128">EE0</font></span></a></span>;<br/><a NAME="E9:213_1_1_1"/>
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">T1</font> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c23">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c24">T1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c1">S</font></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> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c25">T2</font> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c23">r</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c25">T2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c1">S</font></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> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a>, <a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/><a NAME="E10:213_1_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c24">T1</font> is    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c23">r</font></span>)</span></span>)</span></span>)</span>,<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> <font color="Maroon" title="c1">S</font></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>) &amp; <font color="Maroon" title="c25">T2</font> is    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c23">r</font></span>)</span></span>)</span></span>)</span>,<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> <font color="Maroon" title="c1">S</font></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>) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D2" title="FUNCT_2:def.2">FUNCT_2:def 2</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c37">TT1</font> = <font color="Maroon" title="c24">T1</font>, <font color="Maroon" title="c38">TT2</font> = <font color="Maroon" title="c25">T2</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c23">r</font></span>)</span></span>)</span></span>)</span>,<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> <font color="Maroon" title="c1">S</font></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> ;<br/><a NAME="E12:213_1_1_1"/>
( <font color="Maroon" title="c24">T1</font> is <font color="Maroon" title="c36">k1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c35">h</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  &amp; <font color="Maroon" title="c25">T2</font> is <font color="Maroon" title="c36">k1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c35">h</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  )
 ;<br/><a NAME="E13:213_1_1_1"/><span class="kw">then </span>
( <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c24">T1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c36">k1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c25">T2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c36">k1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c1">S</font></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/><a NAME="E14:213_1_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c24">T1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c33">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c1">S</font> &amp; <font color="Maroon" title="c25">T2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c33">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c1">S</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T60" title="ZFMISC_1:th.60">ZFMISC_1:60</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c39">t1</font> = <font color="Maroon" title="c24">T1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c33">k</font>, <font color="Maroon" title="c40">t2</font> = <font color="Maroon" title="c25">T2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c33">k</font> as   <a href="fomodel1.html#V13" title="FOMODEL1:attr.13">termal</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c1">S</font> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c41">z</font> = <span class="p1">(<span class="default"><span class="p2"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c39">t1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c40">t2</font> as   <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c1">S</font> ;<br/><a NAME="E17:213_1_1_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">TT1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c34">kk</font></span>)</span></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c37">TT1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c34">kk</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c38">TT2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c34">kk</font></span>)</span></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c38">TT2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c34">kk</font></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/><a NAME="E18:213_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E130">E1</font></span>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c37">TT1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c34">kk</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c37">TT1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c34">kk</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c38">TT2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c34">kk</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c38">TT2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c34">kk</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T29" title="FOMODEL0:th.29">FOMODEL0:29</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c42">ST</font> = <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c39">t1</font>,<font color="Maroon" title="c40">t2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>;<br/><a NAME="E19:213_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">TT1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c34">kk</font></span>)</span></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c38">TT2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c34">kk</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c29">Fam</font>
 ;<br/><a NAME="E20:213_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c41">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D42" title="FOMODEL2:def.42">FOMODEL2:def 42</a></span>;<br/><span class="kw">hence </span><a NAME="E21:213_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c24">T1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c33">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c25">T2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c33">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:213_1_1_1"><span class="lab"><font color="Green" title="E130">E1</font></span></a>, <a class="txt" href="fomodel4.html#E140"><span class="lab"><font color="Green" title="E110">Lm36</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="213_1_1_2"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:213_1_1_2"/>
( <font color="Maroon" title="c28">rr</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="c1">S</font> or <font color="Maroon" title="c28">rr</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="213_1_1_2_1"><span class="kw">suppose </span></a><a NAME="E1:213_1_1_2_1"/>
<font color="Maroon" title="c28">rr</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="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="Olive">b<sub>2</sub></font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><div class="add"><a NAME="E2:213_1_1_2_1"/>
<font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Maroon" title="c26">psi0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Maroon" title="c27">phi1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:213_1_1"><span class="lab"><font color="Green" title="E124">D3</font></span></a>, <a class="txt" href="#E20:213_1_1"><span class="lab"><font color="Green" title="E127">DD5</font></span></a>, <a class="txt" href="#E17:213_1_1"><span class="lab"><font color="Green" title="E125">D4</font></span></a>, <a class="ref" href="finseq_1.html#T14" title="FINSEQ_1:th.14">FINSEQ_1:14</a></span>;<br/><span class="kw">hence </span><a NAME="E3:213_1_1_2_1"/>
<font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c17">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:213_1_1"><span class="lab"><font color="Green" title="E126">DD6</font></span></a>, <a class="ref" href="fomodel2.html#T27" title="FOMODEL2:th.27">FOMODEL2:27</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="213_1_1_2_2"><span class="kw">suppose </span></a><a NAME="E1:213_1_1_2_2"/>
<font color="Maroon" title="c28">rr</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</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="Olive">b<sub>2</sub></font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><div class="add"><a NAME="E2:213_1_1_2_2"/>
<font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Maroon" title="c26">psi0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Maroon" title="c27">phi1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:213_1_1"><span class="lab"><font color="Green" title="E124">D3</font></span></a>, <a class="txt" href="#E20:213_1_1"><span class="lab"><font color="Green" title="E127">DD5</font></span></a>, <a class="txt" href="#E17:213_1_1"><span class="lab"><font color="Green" title="E125">D4</font></span></a>, <a class="ref" href="finseq_1.html#T14" title="FINSEQ_1:th.14">FINSEQ_1:14</a></span>;<br/><span class="kw">hence </span><a NAME="E3:213_1_1_2_2"/>
<font color="Maroon" title="c15">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c17">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:213_1_1"><span class="lab"><font color="Green" title="E126">DD6</font></span></a>, <a class="ref" href="fomodel2.html#T27" title="FOMODEL2:th.27">FOMODEL2:27</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></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:213_1"/>
<span class="p1">(<span class="default"><a href="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">X</font> is <font color="Maroon" title="c1">S</font> <a href="fomodel2.html#V12" title="FOMODEL2:attr.12">-correct</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D44" title="FOMODEL2:def.44">FOMODEL2:def 44</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="E2:213"/>
 <a href="fomodel4.html#K28" title="FOMODEL4:func.28">R3e</a> <font color="Maroon" title="c1">S</font> is  <a href="fomodel4.html#V17" title="FOMODEL4:attr.17">Correct</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D69" target="_self" title="FOMODEL4:def.69">RuleCorr</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/>


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