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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">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> <br/>  for <font color="Olive" title="b2">phi1</font>, <font color="Olive" title="b3">phi2</font> being   <a href="fomodel2.html#V4" title="FOMODEL2:attr.4">wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b4">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font> holds <br/> ( <font color="Olive" title="b4">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p4">(<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="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Olive" title="b2">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Olive" title="b3">phi2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  iff ( <font color="Olive" title="b4">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive" title="b2">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  &amp; <font color="Olive" title="b4">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive" title="b3">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">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">  for <font color="Olive" title="b1">phi1</font>, <font color="Olive" title="b2">phi2</font> being   <a href="fomodel2.html#V4" title="FOMODEL2:attr.4">wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b3">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font> holds <br/> ( <font color="Olive" title="b3">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p4">(<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="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Olive" title="b1">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Olive" title="b2">phi2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  iff ( <font color="Olive" title="b3">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive" title="b1">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  &amp; <font color="Olive" title="b3">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive" title="b2">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">phi1</font>, <font color="Maroon" title="c4">phi2</font> be   <a href="fomodel2.html#V4" title="FOMODEL2:attr.4">wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c1">S</font> holds <br/> ( <font color="Olive" title="b1">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p4">(<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="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c4">phi2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  iff ( <font color="Olive" title="b1">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c3">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  &amp; <font color="Olive" title="b1">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c4">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">I</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">U</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"> ( <font color="Maroon" title="c5">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p4">(<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="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c4">phi2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  iff ( <font color="Maroon" title="c5">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c3">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  &amp; <font color="Maroon" title="c5">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c4">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  ) )</span><br/>









<span class="kw">set </span><font color="Maroon" title="c6">Nor</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="c7">II</font> = <font color="Maroon" title="c2">U</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">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="c9">B</font> =  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">D</font> =  <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">U</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">set </span><font color="Maroon" title="c11">m1</font> =  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">m2</font> =  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font>;<br/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <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">U</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>)) <span class="kw">-&gt; </span>  <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="c2">U</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> =  <a href="fomodel2.html#K19" title="FOMODEL2:func.19">ExIterator</a> $1;<br/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>2</sub></font>(   <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">U</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>)) <span class="kw">-&gt; </span>  <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="c2">U</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> =  <a href="fomodel2.html#K21" title="FOMODEL2:func.21">NorIterator</a> $1;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">F</font> = (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</font>) <a href="fomodel2.html#K22" title="FOMODEL2:func.22">-TruthEval</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">m</font> =  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>);<br/>
<span class="kw">set </span><font color="Maroon" title="c15">M</font> = <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c16">d1</font> = <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>, <font color="Maroon" title="c17">d2</font> = <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span> as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> ;<br/>
<a NAME="E2:158"/>
( <font color="Maroon" title="c3">phi1</font> is <span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c16">d1</font></span>)</span> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  &amp; <font color="Maroon" title="c4">phi2</font> is <span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c17">d2</font></span>)</span> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D31" target="_self" title="FOMODEL2:def.31">DefDepth</a></span>;<br/>
<a NAME="E3:158"/><span class="kw">then </span>
( <font color="Maroon" title="c3">phi1</font> is <span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c16">d1</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  &amp; <font color="Maroon" title="c4">phi2</font> is <span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c17">d2</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  )
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c18">phi11</font> = <font color="Maroon" title="c3">phi1</font>, <font color="Maroon" title="c19">phi22</font> = <font color="Maroon" title="c4">phi2</font> as   <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>) <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c1">S</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c20">phi</font> = <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="c1">S</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c18">phi11</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c19">phi22</font> as  <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c1">S</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c21">mm</font> =  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p1">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>), <font color="Maroon" title="c22">MM</font> = <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span> <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">set </span><font color="Maroon" title="c23">Phim</font> = <font color="Maroon" title="c1">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c24">PhiM</font> = <font color="Maroon" title="c1">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p3">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p3">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span> <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="c25">FM</font> = (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p3">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p3">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span> <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="c26">Fm</font> = (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c27">mNF</font> = <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span> <a href="fomodel2.html#K35" title="FOMODEL2:func.35">-NorFormulasOf</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="lab"><font color="Green" title="E69">B4</font></span>: <font color="Maroon" title="c5">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c3">phi1</font> = 
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">I</font>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p3">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p3">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">phi11</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D26" target="_self" title="FOMODEL2:def.26">DefTruth4</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p3">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p3">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c3">phi1</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel2.html#E81"><span class="lab"><font color="Green" title="E64">Lm41</font></span></a></span>
;<br/>
<span class="lab"><font color="Green" title="E70">Z1</font></span>: <font color="Maroon" title="c5">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c19">phi22</font> = 
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">I</font>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p3">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p3">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">phi22</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D26" target="_self" title="FOMODEL2:def.26">DefTruth4</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p3">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p3">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c4">phi2</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel2.html#E81"><span class="lab"><font color="Green" title="E64">Lm41</font></span></a></span>
;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c28">phi111</font> = <font color="Maroon" title="c18">phi11</font>, <font color="Maroon" title="c29">phi222</font> = <font color="Maroon" title="c19">phi22</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D24" target="_self" title="FOMODEL2:def.24">DefWff1</a></span>;<br/>
<a NAME="E10:158"/>
<font color="Maroon" title="c20">phi</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="c1">S</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c28">phi111</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c29">phi222</font>
 
;<br/>
<a NAME="E11:158"/><span class="kw">then </span>
<font color="Maroon" title="c20">phi</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span> <a href="fomodel2.html#K35" title="FOMODEL2:func.35">-NorFormulasOf</a> <font color="Maroon" title="c1">S</font>
 
;<br/>
<a NAME="E12:158"/><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="c5">I</font>,<font color="Maroon" title="c20">phi</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> <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">U</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"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p4">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p4">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span> <a href="fomodel2.html#K35" title="FOMODEL2:func.35">-NorFormulasOf</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="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/>
<a NAME="E13:158"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">B5</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c20">phi</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">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p3">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p4">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p4">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel2.html#E56"><span class="lab"><font color="Green" title="E42">Lm33</font></span></a></span>;<br/>
<a NAME="E14:158"/><span class="lab"><font color="Green" title="E72">B6</font></span>: 
<span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</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="c22">MM</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel2.html#K19" title="FOMODEL2:func.19">ExIterator</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</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="c21">mm</font></span>)</span></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> <span class="p3">(<span class="default"><span class="p4">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</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="c21">mm</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</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="c21">mm</font></span>)</span>
 
<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="E15:158"/>
(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span> 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="c2">U</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"><font color="Maroon" title="c1">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <span class="p3">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p4">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p4">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</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>)
 
<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="c30">Fmm</font> = (<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span> 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="c2">U</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"><font color="Maroon" title="c1">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <span class="p3">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p4">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p4">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</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="E17:158"/><span class="lab"><font color="Green" title="E73">B7</font></span>: 
 not <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c20">phi</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="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</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="c21">mm</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="158_3"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:158_3"/><span class="lab"><font color="Green" title="E74">Z3</font></span>: 
 not <font color="Maroon" title="c20">phi</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D24" target="_self" title="FOMODEL2:def.24">DefWff1</a></span>;<br/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</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="c21">mm</font></span>)</span> = 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c30">Fmm</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/>.= 
<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">U</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"><font color="Maroon" title="c1">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <span class="p3">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p4">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p4">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span></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">hence </span><a NAME="E3:158_3"/>
 not <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c20">phi</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="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</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="c21">mm</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:158_3"><span class="lab"><font color="Green" title="E74">Z3</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="E18:158"/><span class="lab"><font color="Green" title="E74">Z4</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c30">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="c2">U</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"><font color="Maroon" title="c1">S</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-formulasOfMaxDepth</a> <span class="p3">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p4">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p4">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span></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/>
<font color="Maroon" title="c5">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c20">phi</font> = 
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">I</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p4">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p4">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="fomodel2.html#K24" title="FOMODEL2:func.24">-TruthEval</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">phi</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D26" target="_self" title="FOMODEL2:def.26">DefTruth4</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p4">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p4">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c20">phi</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="fomodel2.html#E81"><span class="lab"><font color="Green" title="E64">Lm41</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</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="c22">MM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c20">phi</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="ref" href="fomodel2.html#D21" target="_self" title="FOMODEL2:def.21">DefTruth2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel2.html#K19" title="FOMODEL2:func.19">ExIterator</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</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="c21">mm</font></span>)</span></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> <span class="p3">(<span class="default"><span class="p4">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</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="c21">mm</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c20">phi</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="#E14:158"><span class="lab"><font color="Green" title="E72">B6</font></span></a>, <a class="txt" href="#E17:158"><span class="lab"><font color="Green" title="E73">B7</font></span></a>, <a class="ref" href="funct_4.html#T11" title="FUNCT_4:th.11">FUNCT_4:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel2.html#K19" title="FOMODEL2:func.19">ExIterator</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</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="c21">mm</font></span>)</span></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> <span class="p3">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p4">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p5">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p5">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c20">phi</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="ref" href="fomodel2.html#D21" target="_self" title="FOMODEL2:def.21">DefTruth2</a></span>
<br/>.= 
<font color="Maroon">H<sub>2</sub></font>((<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p2">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span>) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c20">phi</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:158"><span class="lab"><font color="Green" title="E71">B5</font></span></a>, <a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">U</font>) <a href="fomodel2.html#K23" title="FOMODEL2:func.23">-TruthEval</a> <span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p3">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c3">phi1</font></span>)</span>,<span class="p3">(<span class="default"><a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c4">phi2</font></span>)</span>)</span>)</span></span>)</span> <a href="fomodel2.html#K20" title="FOMODEL2:func.20">-NorFunctor</a> (<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c20">phi</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:158"><span class="lab"><font color="Green" title="E71">B5</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="E20:158"/>
( <font color="Maroon" title="c5">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p4">(<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="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c3">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c4">phi2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  iff ( <font color="Maroon" title="c5">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c3">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  &amp; <font color="Maroon" title="c5">I</font> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c4">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:158"><span class="lab"><font color="Green" title="E74">Z4</font></span></a>, <a class="txt" href="fomodel2.html#E84"><span class="lab"><font color="Green" title="E67">Lm38</font></span></a>, <a class="txt" href="#E8:158"><span class="lab"><font color="Green" title="E70">Z1</font></span></a>, <a class="txt" href="#E7:158"><span class="lab"><font color="Green" title="E69">B4</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/>


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