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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">l</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="b2">phi0</font> being   <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/>  for <font color="Olive" title="b3">tt</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c1">S</font> holds  (<font color="Olive" title="b1">l</font>,<font color="Olive" title="b3">tt</font>) <a href="fomodel3.html#K26" title="FOMODEL3:func.26">AtomicSubst</a> <font color="Olive" title="b2">phi0</font> is   <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><br/><span class="kw">let </span><font color="Maroon" title="c2">l</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">phi0</font> being   <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/>  for <font color="Olive" title="b2">tt</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c1">S</font> holds  (<font color="Maroon" title="c2">l</font>,<font color="Olive" title="b2">tt</font>) <a href="fomodel3.html#K26" title="FOMODEL3:func.26">AtomicSubst</a> <font color="Olive" title="b1">phi0</font> is   <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><br/><span class="kw">let </span><font color="Maroon" title="c3">phi0</font> be   <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>; <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">tt</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c1">S</font> holds  (<font color="Maroon" title="c2">l</font>,<font color="Olive" title="b1">tt</font>) <a href="fomodel3.html#K26" title="FOMODEL3:func.26">AtomicSubst</a> <font color="Maroon" title="c3">phi0</font> is   <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><br/><span class="kw">let </span><font color="Maroon" title="c4">tt</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (<font color="Maroon" title="c2">l</font>,<font color="Maroon" title="c4">tt</font>) <a href="fomodel3.html#K26" title="FOMODEL3:func.26">AtomicSubst</a> <font color="Maroon" title="c3">phi0</font> is   <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><br/>







<span class="kw">set </span><font color="Maroon" title="c5">ST</font> =  <a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c3">phi0</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">FI</font> = (<font color="Maroon" title="c1">S</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">I</font> = (<font color="Maroon" title="c2">l</font>,<font color="Maroon" title="c4">tt</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">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="c9">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="c10">r</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="c3">phi0</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">n</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> <font color="Maroon" title="c3">phi0</font></span>)</span></span>)</span>;<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">set </span><font color="Maroon" title="c13">TE</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c2">l</font>,<font color="Maroon" title="c4">tt</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c1">S</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">SS</font> =  <a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c15">STT</font> =  <a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c3">phi0</font> as    <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/>
<span class="kw">reconsider </span><font color="Maroon" title="c16">newterms</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c2">l</font>,<font color="Maroon" title="c4">tt</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c1">S</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c15">STT</font> as    <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> ;<br/>
<a NAME="E3:118"/><span class="lab"><font color="Green" title="E49">XX</font></span>: 
<font color="Maroon" title="c16">newterms</font> is    <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="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>, <a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c17">newtermss</font> = <font color="Maroon" title="c16">newterms</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</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> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>, <a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c18">IT</font> = <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> <font color="Maroon" title="c3">phi0</font></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> <font color="Maroon" title="c17">newtermss</font></span>)</span> as   <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="ref" href="fomodel0.html#T30" title="FOMODEL0:th.30">FOMODEL0:30</a></span>;<br/>
<a NAME="E6:118"/>
<font color="Maroon" title="c18">IT</font> is  <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D35" title="FOMODEL1:def.35">FOMODEL1:def 35</a>, <a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a>, <a class="txt" href="#E3:118"><span class="lab"><font color="Green" title="E49">XX</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:118"/>
(<font color="Maroon" title="c2">l</font>,<font color="Maroon" title="c4">tt</font>) <a href="fomodel3.html#K26" title="FOMODEL3:func.26">AtomicSubst</a> <font color="Maroon" title="c3">phi0</font> is   <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>
 ; <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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