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<span class="kw">set </span><font color="Maroon" title="c6">a</font> =  the <a href="fomodel1.html#U1" title="FOMODEL1:sel.1">adicity</a> of <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">EQ</font> =  <a href="fomodel1.html#K18" title="FOMODEL1:func.18">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">d</font> = <font color="Maroon" title="c2">U</font> <a href="fomodel2.html#K2" title="FOMODEL2:func.2">-deltaInterpreter</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">g</font> = <span class="p1">(<span class="default"><a href="fomodel1.html#K18" title="FOMODEL1:func.18">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">U</font> <a href="fomodel2.html#K2" title="FOMODEL2:func.2">-deltaInterpreter</a></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">n</font> =  <a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c5">s</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">A</font> =  <a href="fomodel1.html#K17" title="FOMODEL1:func.17">AtomicFormulaSymbolsOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">O</font> =  <a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">sss</font> = <font color="Maroon" title="c5">s</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K17" title="FOMODEL1:func.17">AtomicFormulaSymbolsOf</a> <font color="Maroon" title="c1">S</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D20" title="FOMODEL1:def.20">FOMODEL1:def 20</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">EQQ</font> =  <a href="fomodel1.html#K18" title="FOMODEL1:func.18">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/>
<a NAME="E3:42_1_1"/>
 <a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <font color="Maroon" title="c14">EQQ</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D23" title="FOMODEL1:def.23">FOMODEL1:def 23</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E16">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">EQQ</font></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="E5:42_1_1"/><span class="lab"><font color="Green" title="E17">B2</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">I</font> <a href="fomodel2.html#K11" title="FOMODEL2:func.11">===</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D12" target="_self" title="FOMODEL2:def.12">DefExtension</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_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="E1:42_1_1_2"/>
( <font color="Maroon" title="c5">s</font> is  <a href="fomodel1.html#V9" title="FOMODEL1:attr.9">own</a>  or  not <font color="Maroon" title="c5">s</font> is  <a href="fomodel1.html#V9" title="FOMODEL1:attr.9">own</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_2_1"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_2_1"/>
<font color="Maroon" title="c5">s</font> is  <a href="fomodel1.html#V9" title="FOMODEL1:attr.9">own</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="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s</font> is    <a href="fomodel2.html#M2" title="FOMODEL2:mode.2">Interpreter</a> of <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c2">U</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">ss</font> = <font color="Maroon" title="c5">s</font> as   <a href="fomodel1.html#V9" title="FOMODEL1:attr.9">own</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> ;<br/><a NAME="E3:42_1_1_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="fomodel2.html#K11" title="FOMODEL2:func.11">===</a></span>)</span> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <font color="Maroon" title="c15">ss</font> is    <a href="fomodel2.html#M2" title="FOMODEL2:mode.2">Interpreter</a> of <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c2">U</font>
 ;<br/><span class="kw">hence </span><a NAME="E4:42_1_1_2_1"/>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s</font> is    <a href="fomodel2.html#M2" title="FOMODEL2:mode.2">Interpreter</a> of <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c2">U</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D12" target="_self" title="FOMODEL2:def.12">DefExtension</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="42_1_1_2_2"><span class="kw">suppose </span></a><a NAME="E1:42_1_1_2_2"/>
 not <font color="Maroon" title="c5">s</font> is  <a href="fomodel1.html#V9" title="FOMODEL1:attr.9">own</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="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s</font> is    <a href="fomodel2.html#M2" title="FOMODEL2:mode.2">Interpreter</a> of <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c2">U</font></span><br/><div class="add"><a NAME="E2:42_1_1_2_2"/><span class="kw">then </span>
 not <font color="Maroon" title="c13">sss</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c1">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D19" title="FOMODEL1:def.19">FOMODEL1:def 19</a></span>;<br/><a NAME="E3:42_1_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c13">sss</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K17" title="FOMODEL1:func.17">AtomicFormulaSymbolsOf</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Maroon" title="c1">S</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E4:42_1_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c13">sss</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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"><a href="fomodel1.html#K18" title="FOMODEL1:func.18">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#T9" title="FOMODEL1:th.9">FOMODEL1:9</a></span>;<br/><a NAME="E5:42_1_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel1.html#K18" title="FOMODEL1:func.18">TheEqSymbOf</a> <font color="Maroon" title="c1">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E6:42_1_1_2_2"/><span class="kw">then </span>
( <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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="c5">s</font></span>)</span></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c2">U</font></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> &amp; <font color="Maroon" title="c5">s</font> is  <a href="fomodel1.html#V7" title="FOMODEL1:attr.7">relational</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_1_1"><span class="lab"><font color="Green" title="E16">B1</font></span></a>, <a class="txt" href="#E5:42_1_1"><span class="lab"><font color="Green" title="E17">B2</font></span></a>, <a class="ref" href="funct_7.html#T94" title="FUNCT_7:th.94">FUNCT_7:94</a></span>;<br/><span class="kw">hence </span><a NAME="E7:42_1_1_2_2"/>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s</font> is    <a href="fomodel2.html#M2" title="FOMODEL2:mode.2">Interpreter</a> of <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c2">U</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D2" target="_self" title="FOMODEL2:def.2">DefInterpreter1</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>

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