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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">U1</font>, <font color="Olive" title="b2">U2</font> being   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/>  for <font color="Olive" title="b3">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><br/>  for <font color="Olive" title="b4">I1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b1">U1</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="b5">I2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b2">U2</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="b6">w</font> being   <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="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b4">I1</font>,<font color="Olive" title="b6">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Olive" title="b1">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Olive" title="b3">m</font></span>)</span> holds <br/><span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b5">I2</font>,<font color="Olive" title="b6">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Olive" title="b2">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Olive" title="b3">m</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">U1</font>, <font color="Maroon" title="c3">U2</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">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><br/>  for <font color="Olive" title="b2">I1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">U1</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="b3">I2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">U2</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="b4">w</font> being   <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="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b2">I1</font>,<font color="Olive" title="b4">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Olive" title="b1">m</font></span>)</span> holds <br/><span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b3">I2</font>,<font color="Olive" title="b4">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Olive" title="b1">m</font></span>)</span></span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">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="c5">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="c6">II1</font> = <font color="Maroon" title="c2">U1</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">II2</font> = <font color="Maroon" title="c3">U2</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">AF</font> =  <a href="fomodel1.html#K32" title="FOMODEL1:func.32">AtomicFormulasOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <span class="kw">means </span> for <font color="Olive" title="b1">I1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">U1</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">I2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">U2</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="b3">w</font> being   <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="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b1">I1</font>,<font color="Olive" title="b3">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> $1</span>)</span> holds <br/><span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b2">I2</font>,<font color="Olive" title="b3">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> $1</span>)</span>;<br/>
<a NAME="E1:61"/><span class="lab"><font color="Green" title="E27">B0</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">set </span><font color="Maroon" title="c9">f1</font> = (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">f2</font> = (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">Z</font> =  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">g1</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K22" title="FOMODEL2:func.22">-TruthEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c11">Z</font> as    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K4" title="RFUNCT_3:func.4">PFuncs</a> (<span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">U1</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="p3"><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><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>) ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">g2</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K22" title="FOMODEL2:func.22">-TruthEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c11">Z</font> as    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K4" title="RFUNCT_3:func.4">PFuncs</a> (<span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">U2</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="p3"><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><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>) ;<br/>
<a NAME="E4:61_1"/><span class="lab"><font color="Green" title="E28">D1</font></span>: 
( (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c12">g1</font> &amp; (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c13">g2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D21" target="_self" title="FOMODEL2:def.21">DefTruth2</a></span>;<br/>
<a NAME="E5:61_1"/><span class="lab"><font color="Green" title="E29">D2</font></span>: 
( <font color="Maroon" title="c12">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S</font> <a href="fomodel2.html#K17" title="FOMODEL2:func.17">-TruthEval</a> <font color="Maroon" title="c2">U1</font> &amp; <font color="Maroon" title="c13">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S</font> <a href="fomodel2.html#K17" title="FOMODEL2:func.17">-TruthEval</a> <font color="Maroon" title="c3">U2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D20" target="_self" title="FOMODEL2:def.20">DefTruth1</a></span>;<br/>
<a NAME="E6:61_1"/><span class="lab"><font color="Green" title="E30">D3</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">U1</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel1.html#K32" title="FOMODEL1:func.32">AtomicFormulasOf</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:61_1"><span class="lab"><font color="Green" title="E28">D1</font></span></a>, <a class="txt" href="#E5:61_1"><span class="lab"><font color="Green" title="E29">D2</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E7:61_1"/><span class="lab"><font color="Green" title="E31">D4</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">U2</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel1.html#K32" title="FOMODEL1:func.32">AtomicFormulasOf</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:61_1"><span class="lab"><font color="Green" title="E28">D1</font></span></a>, <a class="txt" href="#E5:61_1"><span class="lab"><font color="Green" title="E29">D2</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c14">I1</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">U1</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">I2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">U2</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">w</font> being   <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="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c14">I1</font>,<font color="Olive" title="b2">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> holds <br/><span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b1">I2</font>,<font color="Olive" title="b2">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c15">I2</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">U2</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">w</font> being   <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="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c14">I1</font>,<font color="Olive" title="b1">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> holds <br/><span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c15">I2</font>,<font color="Olive" title="b1">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c16">w</font> be   <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="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c14">I1</font>,<font color="Maroon" title="c16">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> implies <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c15">I2</font>,<font color="Maroon" title="c16">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> )</span><br/>





<span class="kw">assume </span><a NAME="E8:61_1"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c14">I1</font>,<font color="Maroon" title="c16">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></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"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c15">I2</font>,<font color="Maroon" title="c16">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span></span><br/>

<a NAME="E9:61_1"/><span class="kw">then </span>
( <font color="Maroon" title="c14">I1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">U1</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font> &amp; <font color="Maroon" title="c16">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fomodel1.html#K32" title="FOMODEL1:func.32">AtomicFormulasOf</a> <font color="Maroon" title="c1">S</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:61_1"><span class="lab"><font color="Green" title="E30">D3</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:61_1"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c15">I2</font>,<font color="Maroon" title="c16">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:61_1"><span class="lab"><font color="Green" title="E31">D4</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</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>
<a NAME="E2:61"/><span class="lab"><font color="Green" title="E28">B1</font></span>: 
 for <font color="Olive" title="b1">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">n</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"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c9">n</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1] )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c10">nn</font> = <font color="Maroon" title="c9">n</font>, <font color="Maroon" title="c11">NN</font> = <font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:61_2"/><span class="lab"><font color="Green" title="E29">C0</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c9">n</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">S<sub>1</sub></font>[<font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]</span><br/>

<span class="kw">let </span><font color="Maroon" title="c12">I1</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">U1</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">I2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">U2</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">w</font> being   <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="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">I1</font>,<font color="Olive" title="b2">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> holds <br/><span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b1">I2</font>,<font color="Olive" title="b2">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c13">I2</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">U2</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">w</font> being   <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="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">I1</font>,<font color="Olive" title="b1">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> holds <br/><span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c13">I2</font>,<font color="Olive" title="b1">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c14">f1n</font> = (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">f1N</font> = (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">f2n</font> = (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">f2N</font> = (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/>
<a NAME="E3:61_2"/><span class="lab"><font color="Green" title="E30">C11</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p3">(<span class="default"><a href="fomodel2.html#K19" title="FOMODEL2:func.19">ExIterator</a> <span class="p4">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p3">(<span class="default"><a href="fomodel2.html#K21" title="FOMODEL2:func.21">NorIterator</a> <span class="p4">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c18">g1N</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K22" title="FOMODEL2:func.22">-TruthEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c11">NN</font> as    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K4" title="RFUNCT_3:func.4">PFuncs</a> (<span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">U1</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="p3"><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><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>) ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c19">g1n</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K22" title="FOMODEL2:func.22">-TruthEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c10">nn</font> as    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K4" title="RFUNCT_3:func.4">PFuncs</a> (<span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">U1</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="p3"><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><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>) ;<br/>
<a NAME="E3:61_2_1"/><span class="lab"><font color="Green" title="E31">D1</font></span>: 
( (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c19">g1n</font> &amp; (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c18">g1N</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D21" target="_self" title="FOMODEL2:def.21">DefTruth2</a></span>;<br/>
<a NAME="E4:61_2_1"/><span class="kw">then </span>
(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel2.html#K19" title="FOMODEL2:func.19">ExIterator</a> <font color="Maroon" title="c19">g1n</font></span>)</span> <a href="funct_4.html#K7" title="FUNCT_4:func.7">+*</a> <span class="p2">(<span class="default"><a href="fomodel2.html#K21" title="FOMODEL2:func.21">NorIterator</a> <font color="Maroon" title="c19">g1n</font></span>)</span></span>)</span> <a href="funct_4.html#K7" title="FUNCT_4:func.7">+*</a> <font color="Maroon" title="c19">g1n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D20" target="_self" title="FOMODEL2:def.20">DefTruth1</a></span>;<br/>
<span class="kw">then </span> <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fomodel2.html#K19" title="FOMODEL2:func.19">ExIterator</a> <font color="Maroon" title="c19">g1n</font></span>)</span> <a href="funct_4.html#K7" title="FUNCT_4:func.7">+*</a> <span class="p3">(<span class="default"><a href="fomodel2.html#K21" title="FOMODEL2:func.21">NorIterator</a> <font color="Maroon" title="c19">g1n</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c19">g1n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p3">(<span class="default"><a href="fomodel2.html#K19" title="FOMODEL2:func.19">ExIterator</a> <font color="Maroon" title="c19">g1n</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p3">(<span class="default"><a href="fomodel2.html#K21" title="FOMODEL2:func.21">NorIterator</a> <font color="Maroon" title="c19">g1n</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c19">g1n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E6:61_2_1"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p3">(<span class="default"><a href="fomodel2.html#K19" title="FOMODEL2:func.19">ExIterator</a> <span class="p4">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p3">(<span class="default"><a href="fomodel2.html#K21" title="FOMODEL2:func.21">NorIterator</a> <span class="p4">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:61_2_1"><span class="lab"><font color="Green" title="E31">D1</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>
<a NAME="E4:61_2"/><span class="lab"><font color="Green" title="E31">C12</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p3">(<span class="default"><a href="fomodel2.html#K19" title="FOMODEL2:func.19">ExIterator</a> <span class="p4">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p3">(<span class="default"><a href="fomodel2.html#K21" title="FOMODEL2:func.21">NorIterator</a> <span class="p4">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c18">g2N</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K22" title="FOMODEL2:func.22">-TruthEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c11">NN</font> as    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K4" title="RFUNCT_3:func.4">PFuncs</a> (<span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">U2</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="p3"><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><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>) ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c19">g2n</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K22" title="FOMODEL2:func.22">-TruthEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c10">nn</font> as    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K4" title="RFUNCT_3:func.4">PFuncs</a> (<span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">U2</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="p3"><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><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>) ;<br/>
<a NAME="E3:61_2_2"/><span class="lab"><font color="Green" title="E32">D1</font></span>: 
( (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c19">g2n</font> &amp; (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c18">g2N</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D21" target="_self" title="FOMODEL2:def.21">DefTruth2</a></span>;<br/>
<a NAME="E4:61_2_2"/><span class="kw">then </span>
(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel2.html#K19" title="FOMODEL2:func.19">ExIterator</a> <font color="Maroon" title="c19">g2n</font></span>)</span> <a href="funct_4.html#K7" title="FUNCT_4:func.7">+*</a> <span class="p2">(<span class="default"><a href="fomodel2.html#K21" title="FOMODEL2:func.21">NorIterator</a> <font color="Maroon" title="c19">g2n</font></span>)</span></span>)</span> <a href="funct_4.html#K7" title="FUNCT_4:func.7">+*</a> <font color="Maroon" title="c19">g2n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D20" target="_self" title="FOMODEL2:def.20">DefTruth1</a></span>;<br/>
<span class="kw">then </span> <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fomodel2.html#K19" title="FOMODEL2:func.19">ExIterator</a> <font color="Maroon" title="c19">g2n</font></span>)</span> <a href="funct_4.html#K7" title="FUNCT_4:func.7">+*</a> <span class="p3">(<span class="default"><a href="fomodel2.html#K21" title="FOMODEL2:func.21">NorIterator</a> <font color="Maroon" title="c19">g2n</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c19">g2n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p3">(<span class="default"><a href="fomodel2.html#K19" title="FOMODEL2:func.19">ExIterator</a> <font color="Maroon" title="c19">g2n</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p3">(<span class="default"><a href="fomodel2.html#K21" title="FOMODEL2:func.21">NorIterator</a> <font color="Maroon" title="c19">g2n</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c19">g2n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E6:61_2_2"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p3">(<span class="default"><a href="fomodel2.html#K19" title="FOMODEL2:func.19">ExIterator</a> <span class="p4">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p3">(<span class="default"><a href="fomodel2.html#K21" title="FOMODEL2:func.21">NorIterator</a> <span class="p4">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:61_2_2"><span class="lab"><font color="Green" title="E32">D1</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>
<span class="kw">let </span><font color="Maroon" title="c18">w</font> be   <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="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">I1</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> implies <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c13">I2</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c19">x</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">I1</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>;<br/>
<span class="kw">assume </span><a NAME="E5:61_2"/><span class="lab"><font color="Green" title="E32">Z0</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">I1</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></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"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c13">I2</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_2_3"><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="E1:61_2_3"/>
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">I1</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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="fomodel2.html#K19" title="FOMODEL2:func.19">ExIterator</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span> or <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">I1</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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="fomodel2.html#K21" title="FOMODEL2:func.21">NorIterator</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span> or <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">I1</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:61_2"><span class="lab"><font color="Green" title="E32">Z0</font></span></a>, <a class="txt" href="fomodel2.html#E31"><span class="lab"><font color="Green" title="E25">Lm25</font></span></a>, <a class="txt" href="#E3:61_2"><span class="lab"><font color="Green" title="E30">C11</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_2_3_1"><span class="kw">suppose </span></a><a NAME="E1:61_2_3_1"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">I1</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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="fomodel2.html#K19" title="FOMODEL2:func.19">ExIterator</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></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"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c13">I2</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c20">v</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>, <font color="Maroon" title="c21">ww</font> being   <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c1">S</font><span class="kw"> such that </span><br/><a NAME="E3:61_2_3_1"/><span class="lab"><font color="Green" title="E33">D1</font></span>: 
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">I1</font>,<font color="Maroon" title="c21">ww</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span> &amp; <font color="Maroon" title="c18">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c20">v</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c21">ww</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D17" target="_self" title="FOMODEL2:def.17">DefExIter</a></span>;<br/><a NAME="E4:61_2_3_1"/>
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c13">I2</font>,<font color="Maroon" title="c21">ww</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span> &amp; <font color="Maroon" title="c18">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c20">v</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c21">ww</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:61_2_3_1"><span class="lab"><font color="Green" title="E33">D1</font></span></a>, <a class="txt" href="#E2:61_2"><span class="lab"><font color="Green" title="E29">C0</font></span></a></span>;<br/><a NAME="E5:61_2_3_1"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c13">I2</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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="fomodel2.html#K19" title="FOMODEL2:func.19">ExIterator</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D17" target="_self" title="FOMODEL2:def.17">DefExIter</a></span>;<br/><span class="kw">hence </span><a NAME="E6:61_2_3_1"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c13">I2</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel2.html#E31"><span class="lab"><font color="Green" title="E25">Lm25</font></span></a>, <a class="txt" href="#E4:61_2"><span class="lab"><font color="Green" title="E31">C12</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="61_2_3_2"><span class="kw">suppose </span></a><a NAME="E1:61_2_3_2"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">I1</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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="fomodel2.html#K21" title="FOMODEL2:func.21">NorIterator</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></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"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c13">I2</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c20">phi1</font>, <font color="Maroon" title="c21">phi2</font> being   <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c1">S</font><span class="kw"> such that </span><br/><a NAME="E3:61_2_3_2"/><span class="lab"><font color="Green" title="E33">D1</font></span>: 
( <font color="Maroon" title="c18">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c20">phi1</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c21">phi2</font> &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">I1</font>,<font color="Maroon" title="c20">phi1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span> &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">I1</font>,<font color="Maroon" title="c21">phi2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D19" target="_self" title="FOMODEL2:def.19">DefNorIter</a></span>;<br/><a NAME="E4:61_2_3_2"/>
( <font color="Maroon" title="c18">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c1">S</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c20">phi1</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c21">phi2</font> &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c13">I2</font>,<font color="Maroon" title="c20">phi1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span> &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c13">I2</font>,<font color="Maroon" title="c21">phi2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:61_2_3_2"><span class="lab"><font color="Green" title="E33">D1</font></span></a>, <a class="txt" href="#E2:61_2"><span class="lab"><font color="Green" title="E29">C0</font></span></a></span>;<br/><a NAME="E5:61_2_3_2"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c13">I2</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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="fomodel2.html#K21" title="FOMODEL2:func.21">NorIterator</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D19" target="_self" title="FOMODEL2:def.19">DefNorIter</a></span>;<br/><span class="kw">hence </span><a NAME="E6:61_2_3_2"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c13">I2</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel2.html#E31"><span class="lab"><font color="Green" title="E25">Lm25</font></span></a>, <a class="txt" href="#E4:61_2"><span class="lab"><font color="Green" title="E31">C12</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="61_2_3_3"><span class="kw">suppose </span></a><a NAME="E1:61_2_3_3"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">I1</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U1</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</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"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c13">I2</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:61_2_3_3"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c13">I2</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c9">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:61_2"><span class="lab"><font color="Green" title="E29">C0</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:61_2_3_3"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c13">I2</font>,<font color="Maroon" title="c18">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U2</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel2.html#E31"><span class="lab"><font color="Green" title="E25">Lm25</font></span></a>, <a class="txt" href="#E4:61_2"><span class="lab"><font color="Green" title="E31">C12</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><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="kw">thus </span><a NAME="E3:61"/>
 for <font color="Olive" title="b1">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">m</font>]
 <span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S2" title="NAT_1:sch.2">NAT_1:sch 2</a>(<a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E27">B0</font></span></a>, <a class="txt" href="#E2:61"><span class="lab"><font color="Green" title="E28">B1</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>
