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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">t1</font>, <font color="Olive" title="b2">t2</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  <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="Olive" title="b1">t1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Olive" title="b2">t2</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">t1</font>, <font color="Maroon" title="c3">t2</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"> <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="c2">t1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">t2</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="c4">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="c5">AT</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="c6">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="c7">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="c8">tt1</font> = <font color="Maroon" title="c2">t1</font>, <font color="Maroon" title="c9">tt2</font> = <font color="Maroon" title="c3">t2</font> as    <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> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D32" title="FOMODEL1:def.32">FOMODEL1:def 32</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">T</font> = <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c8">tt1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c9">tt2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> as  2 <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/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">ATT</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/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">TT</font> = <font color="Maroon" title="c10">T</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c11">ATT</font> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">TTT</font> = <font color="Maroon" title="c12">TT</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>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">EE</font> =  <a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font> as   <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> ;<br/>
<span class="lab"><font color="Green" title="E3">B0</font></span>:  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 2</span>)</span> = 
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 2</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></span>
<br/>.= 
2

;<br/>
<a NAME="E8:2"/><span class="lab"><font color="Green" title="E4">B1</font></span>: 
 <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="c14">EE</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:2"><span class="lab"><font color="Green" title="E3">B0</font></span></a>, <a class="ref" href="fomodel1.html#D23" title="FOMODEL1:def.23">FOMODEL1:def 23</a></span>;<br/>
<a NAME="E9:2"/>
<span class="p1">(<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="c12">TT</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<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> 
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">tailer</font> = <span class="p1">(<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="c10">T</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <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="c16">SSS</font> =  <a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c1">S</font> as   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>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">EEE</font> = <font color="Maroon" title="c14">EE</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c16">SSS</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c18">header</font> = <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c17">EEE</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <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="c19">IT</font> = <font color="Maroon" title="c18">header</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c15">tailer</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <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="c20">phi</font> = <font color="Maroon" title="c19">IT</font> 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="fomodel1.html#T13" title="FOMODEL1:th.13">FOMODEL1:13</a></span>;<br/>
<font color="Maroon" title="c15">tailer</font> = 
<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="fomodel0.html#K8" title="FOMODEL0:func.8">-multiCat</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">tt1</font>,<font color="Maroon" title="c9">tt2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>

<br/>.= 
<font color="Maroon" title="c8">tt1</font> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c9">tt2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T15" title="FOMODEL0:th.15">FOMODEL0:15</a></span>
;<br/>
<a NAME="E17:2"/><span class="kw">then </span>
<span class="p1"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p2">(<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="p1">(<span class="default"><font color="Maroon" title="c2">t1</font> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">t2</font></span>)</span> 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 class="kw">by</span> <span class="lab"><a class="txt" href="#E8:2"><span class="lab"><font color="Green" title="E4">B1</font></span></a>, <a class="ref" href="fomodel1.html#D35" title="FOMODEL1:def.35">FOMODEL1:def 35</a></span>;<br/>
<span class="kw">hence </span><a NAME="E18:2"/>
<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="c2">t1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">t2</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 class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T32" title="FINSEQ_1:th.32">FINSEQ_1:32</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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