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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">  for <font color="Olive" title="b1">l1</font>, <font color="Olive" title="b2">l2</font> being   <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b3">t</font> being   <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> holds   <a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <span class="p1">(<span class="default">(<font color="Olive" title="b1">l1</font>,<font color="Olive" title="b2">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Olive" title="b3">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Olive" title="b2">l2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Olive" title="b3">t</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">l1</font>, <font color="Maroon" title="c3">l2</font> be   <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</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">  for <font color="Olive" title="b1">t</font> being   <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> holds   <a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Olive" title="b1">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Olive" title="b1">t</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">t</font> be   <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c4">t</font></span>)</span></span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">s</font> = <font color="Maroon" title="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">newt</font> = (<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">ST</font> =  <a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c4">t</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">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="c9">C</font> = <font color="Maroon" title="c1">S</font> <a href="fomodel1.html#K21" title="FOMODEL1:func.21">-multiCat</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">ST2</font> =  <a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">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="c12">TT</font> =  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">TTT</font> =  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c1">S</font> 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#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> <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="E2:126"/><span class="lab"><font color="Green" title="E53">C0</font></span>: 
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c1">S</font> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c13">TTT</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">TTT</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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="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/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c14">ss</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</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> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</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>,<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> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T2" title="FUNCT_2:th.2">FUNCT_2:2</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1"><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="E1:126_1"/>
(  not <font color="Maroon" title="c4">t</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="fomodel1.html#V14" title="FOMODEL1:attr.14">-termal</a>  or <font color="Maroon" title="c4">t</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="fomodel1.html#V14" title="FOMODEL1:attr.14">-termal</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1"><span class="kw">suppose </span></a><a NAME="E1:126_1_1"/>
 not <font color="Maroon" title="c4">t</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="fomodel1.html#V14" title="FOMODEL1:attr.14">-termal</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c4">t</font></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">s1</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="c4">t</font> as   non  <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>   <a href="fomodel1.html#V10" title="FOMODEL1:attr.10">ofAtomicFormula</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#T16" title="FOMODEL1:th.16">FOMODEL1:16</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c16">h</font> = (<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <span class="p1"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><font color="Maroon" title="c15">s1</font></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> as   <a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c1">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  1 <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> ;<br/><span class="kw">set </span><font color="Maroon" title="c17">s2</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> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</font></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c18">n1</font> =  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c15">s1</font></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c19">n2</font> =  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <span class="p2">(<span class="default"><span class="p3">(<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> <span class="p3">(<span class="default">(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span></span>)</span>;<br/><a NAME="E4:126_1_1"/>
<font color="Maroon" title="c14">ss</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c4">t</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:126"><span class="lab"><font color="Green" title="E53">C0</font></span></a>, <a class="ref" href="relat_1.html#T165" title="RELAT_1:th.165">RELAT_1:165</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">p</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c4">t</font></span>)</span> as   <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="c15">s1</font></span>)</span> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <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="fomodel0.html#T26" title="FOMODEL0:th.26">FOMODEL0:26</a></span>;<br/><a NAME="E6:126_1_1"/><span class="lab"><font color="Green" title="E54">C1</font></span>: 
(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</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"><span class="p2">(<span class="default"><span class="p3">(<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> <span class="p3">(<span class="default">(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span></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_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D37" title="FOMODEL1:def.37">FOMODEL1:def 37</a></span>;<br/><a NAME="E7:126_1_1"/>
<font color="Maroon" title="c4">t</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="c15">s1</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_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D37" title="FOMODEL1:def.37">FOMODEL1:def 37</a></span>;<br/><span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">t</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><font color="Maroon" title="c15">s1</font></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span></span>)</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="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</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_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T36" title="FOMODEL0:th.36">FOMODEL0:36</a></span>
<br/>.= 
<font color="Maroon" title="c16">h</font> <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="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</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_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#D23" title="FOMODEL0:def.23">FOMODEL0:def 23</a></span>
<br/>.= 
<font color="Maroon" title="c16">h</font> <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> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T37" title="FOMODEL0:th.37">FOMODEL0:37</a></span>
;<br/><a NAME="E9:126_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">C2</font></span>: 
(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">h</font> <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="c20">p</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#D23" title="FOMODEL0:def.23">FOMODEL0:def 23</a></span>;<br/><a NAME="E10:126_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c16">h</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"><span class="p2">(<span class="default"><span class="p3">(<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> <span class="p3">(<span class="default">(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> &amp; <font color="Maroon" title="c16">h</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="c15">s1</font></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:126_1_1"><span class="lab"><font color="Green" title="E54">C1</font></span></a>, <a class="ref" href="fomodel0.html#T34" title="FOMODEL0:th.34">FOMODEL0:34</a>, <a class="ref" href="fomodel0.html#T41" title="FOMODEL0:th.41">FOMODEL0:41</a></span>;<br/><a NAME="E11:126_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c16">h</font> <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="c15">s1</font> &amp; <font color="Maroon" title="c16">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T40" title="FINSEQ_1:th.40">FINSEQ_1:40</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c21">pp</font> = <font color="Maroon" title="c20">p</font> as   <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> <span class="p2">(<span class="default"><span class="p3">(<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> <span class="p3">(<span class="default">(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span></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">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></span>;<br/><a NAME="E13:126_1_1"/>
(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</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"><span class="p2">(<span class="default"><span class="p3">(<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> <span class="p3">(<span class="default">(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span></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="c21">pp</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:126_1_1"><span class="lab"><font color="Green" title="E55">C2</font></span></a>, <a class="txt" href="#E6:126_1_1"><span class="lab"><font color="Green" title="E54">C1</font></span></a>, <a class="ref" href="fomodel0.html#T41" title="FOMODEL0:th.41">FOMODEL0:41</a></span>;<br/><span class="kw">hence </span><a NAME="E14:126_1_1"/>
 <a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c4">t</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D37" title="FOMODEL1:def.37">FOMODEL1:def 37</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="126_1_2"><span class="kw">suppose </span></a><a NAME="E1:126_1_2"/>
<font color="Maroon" title="c4">t</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="fomodel1.html#V14" title="FOMODEL1:attr.14">-termal</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c4">t</font></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">t0</font> = <font color="Maroon" title="c4">t</font> as   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="fomodel1.html#V14" title="FOMODEL1:attr.14">-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="c16">newt</font> = (<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c15">t0</font> as   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="fomodel1.html#V14" title="FOMODEL1:attr.14">-termal</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c1">S</font> ;<br/><a NAME="E4:126_1_2"/>
(  <a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c16">newt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c15">t0</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">hence </span><a NAME="E5:126_1_2"/>
 <a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">l1</font>,<font color="Maroon" title="c3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c3">l2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c4">t</font></span>)</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>
