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<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">m</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">  for <font color="Olive" title="b1">S</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b2">U</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>  holds   <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="Olive" title="b1">S</font>,<font color="Olive" title="b2">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Olive" title="b1">S</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="fomodel2.html#K29" title="FOMODEL2:func.29">-NorFormulasOf</a> <font color="Olive" title="b1">S</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">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">U</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>  holds   <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="c2">S</font>,<font color="Olive" title="b1">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="fomodel2.html#K29" title="FOMODEL2:func.29">-NorFormulasOf</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">U</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">  <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="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="fomodel2.html#K29" title="FOMODEL2:func.29">-NorFormulasOf</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">mm</font> = <font color="Maroon" title="c1">m</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">II</font> = <font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">SS</font> =  <a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">N</font> =  <a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">Fm</font> = (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">Phim</font> = <font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">IT</font> =  <a href="fomodel2.html#K21" title="FOMODEL2:func.21">NorIterator</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font></span>)</span>;<br/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>,  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>) <span class="kw">-&gt; </span>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  = <span class="p1">(<span class="default"><span class="p2"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> $1</span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> $2;<br/>
<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[] <span class="kw">means </span>verum;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">A</font> = <span class="p1"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">phi1</font>,<font color="Olive" title="b2">phi2</font>) where <font color="Olive" title="b1">phi1</font>, <font color="Olive" title="b2">phi2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font> : <font color="Maroon">S<sub>1</sub></font>[] </span> } </span> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">LH</font> =  <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="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">RH</font> = <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">phi1</font>,<font color="Olive" title="b2">phi2</font>) where <font color="Olive" title="b1">phi1</font>, <font color="Olive" title="b2">phi2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font> : <font color="Maroon">S<sub>1</sub></font>[] </span> } </span> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/>
<a NAME="E1:87"/>
(<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font> is    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</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">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font></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>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#T8" target="_self" title="FOMODEL2:th.8">Lm32</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c14">Fmm</font> = (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font></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="E3:87"/><span class="lab"><font color="Green" title="E43">B1</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c14">Fmm</font> <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">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</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="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c15">ITT</font> =  <a href="fomodel2.html#K21" title="FOMODEL2:func.21">NorIterator</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font></span>)</span> as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <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">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">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="c2">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="E5:87"/><span class="lab"><font color="Green" title="E44">B2</font></span>: 
<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">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">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="c2">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="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> where <font color="Olive" title="b1">x</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font>, <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c2">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="p1"><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> : verum </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="domain_1.html#T19" title="DOMAIN_1:th.19">DOMAIN_1:19</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="87_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c16">z</font> be    <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"> ( <font color="Maroon" title="c16">z</font> <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="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span> implies <font color="Maroon" title="c16">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">phi1</font>,<font color="Olive" title="b2">phi2</font>) where <font color="Olive" title="b1">phi1</font>, <font color="Olive" title="b2">phi2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font> : <font color="Maroon">S<sub>1</sub></font>[] </span> } </span> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )</span><br/><span class="kw">assume </span><a NAME="E1:87_1"/><span class="lab"><font color="Green" title="E45">D0</font></span>: 
<font color="Maroon" title="c16">z</font> <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="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</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"> <font color="Maroon" title="c16">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">phi1</font>,<font color="Olive" title="b2">phi2</font>) where <font color="Olive" title="b1">phi1</font>, <font color="Olive" title="b2">phi2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font> : <font color="Maroon">S<sub>1</sub></font>[] </span> } </span> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span><br/><a NAME="E2:87_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">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="c2">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>
 ;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c17">x</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font>, <font color="Maroon" title="c18">y</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c2">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="p1"><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 class="kw"> such that </span><br/><a NAME="E4:87_1"/><span class="lab"><font color="Green" title="E46">D1</font></span>: 
<font color="Maroon" title="c16">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c18">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:87"><span class="lab"><font color="Green" title="E44">B2</font></span></a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c19">phi1</font>, <font color="Maroon" title="c20">phi2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c2">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="p1"><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 class="kw"> such that </span><br/><a NAME="E6:87_1"/><span class="lab"><font color="Green" title="E47">D2</font></span>: 
( <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c19">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c20">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="c17">x</font>,<font color="Maroon" title="c19">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="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</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="c17">x</font>,<font color="Maroon" title="c20">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="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</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>, <a class="txt" href="#E1:87_1"><span class="lab"><font color="Green" title="E45">D0</font></span></a>, <a class="txt" href="#E4:87_1"><span class="lab"><font color="Green" title="E46">D1</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c21">phi11</font> = <font color="Maroon" title="c19">phi1</font>, <font color="Maroon" title="c22">phi22</font> = <font color="Maroon" title="c20">phi2</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87_1"><span class="lab"><font color="Green" title="E47">D2</font></span></a>, <a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E43">B1</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">set </span><font color="Maroon" title="c23">yy</font> = <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c21">phi11</font>,<font color="Maroon" title="c22">phi22</font>);<br/><a NAME="E8:87_1"/>
( <font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c21">phi11</font>,<font color="Maroon" title="c22">phi22</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">phi1</font>,<font color="Olive" title="b2">phi2</font>) where <font color="Olive" title="b1">phi1</font>, <font color="Olive" title="b2">phi2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font> : <font color="Maroon">S<sub>1</sub></font>[] </span> } </span>  &amp; <font color="Maroon" title="c16">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c17">x</font>,<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c21">phi11</font>,<font color="Maroon" title="c22">phi22</font>)</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:87_1"><span class="lab"><font color="Green" title="E46">D1</font></span></a>, <a class="txt" href="#E6:87_1"><span class="lab"><font color="Green" title="E47">D2</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E9:87_1"/>
<font color="Maroon" title="c16">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">phi1</font>,<font color="Olive" title="b2">phi2</font>) where <font color="Olive" title="b1">phi1</font>, <font color="Olive" title="b2">phi2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font> : <font color="Maroon">S<sub>1</sub></font>[] </span> } </span> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</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="E7:87"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">B5</font></span>: 
 <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="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">phi1</font>,<font color="Olive" title="b2">phi2</font>) where <font color="Olive" title="b1">phi1</font>, <font color="Olive" title="b2">phi2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font> : <font color="Maroon">S<sub>1</sub></font>[] </span> } </span> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="87_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c16">z</font> be    <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"> ( <font color="Maroon" title="c16">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">phi1</font>,<font color="Olive" title="b2">phi2</font>) where <font color="Olive" title="b1">phi1</font>, <font color="Olive" title="b2">phi2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font> : <font color="Maroon">S<sub>1</sub></font>[] </span> } </span> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> implies <font color="Maroon" title="c16">z</font> <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="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:87_2"/>
<font color="Maroon" title="c16">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">phi1</font>,<font color="Olive" title="b2">phi2</font>) where <font color="Olive" title="b1">phi1</font>, <font color="Olive" title="b2">phi2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font> : <font color="Maroon">S<sub>1</sub></font>[] </span> } </span> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 ; <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="c16">z</font> <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="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c17">xx</font>, <font color="Maroon" title="c18">yy</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:87_2"/><span class="lab"><font color="Green" title="E46">D0</font></span>: 
( <font color="Maroon" title="c17">xx</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font> &amp; <font color="Maroon" title="c18">yy</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">phi1</font>,<font color="Olive" title="b2">phi2</font>) where <font color="Olive" title="b1">phi1</font>, <font color="Olive" title="b2">phi2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font> : <font color="Maroon">S<sub>1</sub></font>[] </span> } </span>  &amp; <font color="Maroon" title="c16">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c17">xx</font>,<font color="Maroon" title="c18">yy</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c19">x</font> = <font color="Maroon" title="c17">xx</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87_2"><span class="lab"><font color="Green" title="E46">D0</font></span></a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c20">phi1</font>, <font color="Maroon" title="c21">phi2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font><span class="kw"> such that </span><br/><a NAME="E6:87_2"/><span class="lab"><font color="Green" title="E47">D1</font></span>: 
<font color="Maroon" title="c18">yy</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c20">phi1</font>,<font color="Maroon" title="c21">phi2</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87_2"><span class="lab"><font color="Green" title="E46">D0</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c22">phi11</font> = <font color="Maroon" title="c20">phi1</font>, <font color="Maroon" title="c23">phi22</font> = <font color="Maroon" title="c21">phi2</font> as   <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c2">S</font> ;<br/><a NAME="E8:87_2"/>
<span class="p1">(<span class="default"><span class="p2"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c22">phi11</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c23">phi22</font> is   <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c2">S</font>
 ;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c24">y</font> = <font color="Maroon" title="c18">yy</font> as   <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c2">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87_2"><span class="lab"><font color="Green" title="E47">D1</font></span></a></span>;<br/><a NAME="E10:87_2"/>
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c19">x</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> <font color="Maroon" title="c14">Fmm</font> &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c19">x</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> <font color="Maroon" title="c14">Fmm</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E43">B1</font></span></a></span>;<br/><a NAME="E11:87_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="c19">x</font>,<font color="Maroon" title="c24">y</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="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87_2"><span class="lab"><font color="Green" title="E47">D1</font></span></a>, <a class="ref" href="fomodel2.html#D19" target="_self" title="FOMODEL2:def.19">DefNorIter</a></span>;<br/><span class="kw">hence </span><a NAME="E12:87_2"/>
<font color="Maroon" title="c16">z</font> <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="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87_2"><span class="lab"><font color="Green" title="E46">D0</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="E9:87"/><span class="kw">then </span>
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">phi1</font>,<font color="Olive" title="b2">phi2</font>) where <font color="Olive" title="b1">phi1</font>, <font color="Olive" title="b2">phi2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <font color="Maroon" title="c1">m</font> : <font color="Maroon">S<sub>1</sub></font>[] </span> } </span> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:87"/>
 <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="c2">S</font>,<font color="Maroon" title="c3">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c2">S</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="fomodel2.html#K29" title="FOMODEL2:func.29">-NorFormulasOf</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:87"><span class="lab"><font color="Green" title="E45">B5</font></span></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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>
