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<span class="kw">let </span><font color="Maroon" title="c1">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">u</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">U</font><br/>  for <font color="Olive" title="b2">S</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b3">l2</font>, <font color="Olive" title="b4">l1</font> being   <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Olive" title="b2">S</font><br/>  for <font color="Olive" title="b5">phi0</font> being   <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Olive" title="b2">S</font><br/>  for <font color="Olive" title="b6">I</font> being  <font color="Olive">b<sub>2</sub></font>,<font color="Maroon" title="c1">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b5">phi0</font> is <span class="p1">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Olive" title="b2">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b3">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  holds <br/><span class="p1">(<span class="default">(<font color="Olive" title="b4">l1</font>,<font color="Olive" title="b1">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b6">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Olive" title="b5">phi0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Olive" title="b3">l2</font>,<font color="Olive" title="b1">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b6">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <span class="p1">(<span class="default">(<font color="Olive" title="b4">l1</font>,<font color="Olive" title="b3">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Olive" title="b5">phi0</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">u</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">U</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">S</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b2">l2</font>, <font color="Olive" title="b3">l1</font> being   <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b4">phi0</font> being   <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b5">I</font> being  <font color="Olive">b<sub>1</sub></font>,<font color="Maroon" title="c1">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b4">phi0</font> is <span class="p1">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Olive" title="b1">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  holds <br/><span class="p1">(<span class="default">(<font color="Olive" title="b3">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b5">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Olive" title="b4">phi0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Olive" title="b2">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b5">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <span class="p1">(<span class="default">(<font color="Olive" title="b3">l1</font>,<font color="Olive" title="b2">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Olive" title="b4">phi0</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">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">l2</font>, <font color="Olive" title="b2">l1</font> being   <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Maroon" title="c3">S</font><br/>  for <font color="Olive" title="b3">phi0</font> being   <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c3">S</font><br/>  for <font color="Olive" title="b4">I</font> being  <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b3">phi0</font> is <span class="p1">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  holds <br/><span class="p1">(<span class="default">(<font color="Olive" title="b2">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b4">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Olive" title="b3">phi0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Olive" title="b1">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b4">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <span class="p1">(<span class="default">(<font color="Olive" title="b2">l1</font>,<font color="Olive" title="b1">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Olive" title="b3">phi0</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">l2</font>, <font color="Maroon" title="c5">l1</font> be   <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Maroon" title="c3">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">phi0</font> being   <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c3">S</font><br/>  for <font color="Olive" title="b2">I</font> being  <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">phi0</font> is <span class="p1">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  holds <br/><span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b2">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Olive" title="b1">phi0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b2">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c4">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Olive" title="b1">phi0</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">phi0</font> be   <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c3">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  <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Maroon" title="c6">phi0</font> is <span class="p1">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  holds <br/><span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Maroon" title="c6">phi0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c4">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c6">phi0</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c7">I</font> be  <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</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="c6">phi0</font> is <span class="p1">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  implies <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Maroon" title="c6">phi0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c4">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c6">phi0</font></span>)</span> )</span><br/>













<span class="kw">set </span><font color="Maroon" title="c8">I1</font> = (<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">I2</font> = (<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">s</font> = <font color="Maroon" title="c5">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c4">l2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">E1</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">E2</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">T</font> = <font color="Maroon" title="c3">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">TT</font> =  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c3">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">SS</font> =  <a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">F</font> = <font color="Maroon" title="c3">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">C</font> = <font color="Maroon" title="c3">S</font> <a href="fomodel1.html#K21" title="FOMODEL1:func.21">-multiCat</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c18">g1</font> = <font color="Maroon" title="c5">l1</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c2">u</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c19">g2</font> = <font color="Maroon" title="c4">l2</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c2">u</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c20">L</font> =  <a href="fomodel1.html#K16" title="FOMODEL1:func.16">LettersOf</a> <font color="Maroon" title="c3">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c21">E</font> =  <a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c3">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c22">d</font> = <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K2" title="FOMODEL2:func.2">-deltaInterpreter</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c23">SSS</font> = <span class="p1">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c24">SSSS</font> = <span class="p1">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c25">psi0</font> = (<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c4">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c6">phi0</font> as   <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c3">S</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c26">r</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">phi0</font>, <font color="Maroon" title="c27">r2</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">psi0</font> as   <a href="fomodel1.html#V7" title="FOMODEL1:attr.7">relational</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Maroon" title="c3">S</font> ;<br/>
<a NAME="E4:129"/>
<font color="Maroon" title="c6">phi0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">r</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T6" title="FOMODEL0:th.6">FOMODEL0:6</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E56">B1</font></span>: <font color="Maroon" title="c26">r</font> = 
<font color="Maroon" title="c25">psi0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T105" title="FUNCT_4:th.105">FUNCT_4:105</a></span>
<br/>.= 
<font color="Maroon" title="c27">r2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T6" title="FOMODEL0:th.6">FOMODEL0:6</a></span>
;<br/>
<a NAME="E6:129"/>
(  not <font color="Maroon" title="c26">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">l1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp;  not <font color="Maroon" title="c26">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E7:129"/><span class="kw">then </span>
(  not <font color="Maroon" title="c26">r</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"><font color="Maroon" title="c5">l1</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c2">u</font></span>)</span></span>)</span> &amp;  not <font color="Maroon" title="c26">r</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"><font color="Maroon" title="c4">l2</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c2">u</font></span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/>
<a NAME="E8:129"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">B2</font></span>: 
( <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c26">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">I</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c26">r</font> &amp; <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c26">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">I</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c26">r</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T11" title="FUNCT_4:th.11">FUNCT_4:11</a></span>;<br/>
<a NAME="E9:129"/>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c3">S</font> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c3">S</font> )
 
<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/>
<a NAME="E10:129"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">B3</font></span>: 
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <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="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a></span>)</span> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c4">l2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c24">SSSS</font> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">SSSS</font> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a>, <a class="ref" href="relat_1.html#T61" title="RELAT_1:th.61">RELAT_1:61</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c28">ST1</font> =  <a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c6">phi0</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a>  ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c29">mm</font> being    <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"> such that </span><br/><a NAME="E13:129"/><span class="lab"><font color="Green" title="E59">B5</font></span>: 
 <a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c6">phi0</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"><font color="Maroon" title="c3">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c29">mm</font></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel3.html#E4"><span class="lab"><font color="Green" title="E3">Lm1</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c30">Tm</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c29">mm</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#T2" title="FOMODEL1:th.2">FOMODEL1:2</a></span>;<br/>
<span class="lab"><font color="Green" title="E60">B6</font></span>:  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c30">Tm</font></span>)</span></span>)</span> = 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c30">Tm</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c30">Tm</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T61" title="RELAT_1:th.61">RELAT_1:61</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c30">Tm</font> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:129"><span class="lab"><font color="Green" title="E58">B3</font></span></a>, <a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c30">Tm</font>

;<br/>
<span class="lab"><font color="Green" title="E61">B8</font></span>:  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c4">l2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c30">Tm</font></span>)</span></span>)</span> = 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c4">l2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c30">Tm</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c30">Tm</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:129"><span class="lab"><font color="Green" title="E58">B3</font></span></a>, <a class="ref" href="relat_1.html#T61" title="RELAT_1:th.61">RELAT_1:61</a></span>
;<br/>
<span class="kw">assume </span><a NAME="E17:129"/>
<font color="Maroon" title="c6">phi0</font> is <span class="p1">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Maroon" title="c6">phi0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c4">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c6">phi0</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c31">R</font> =  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">phi0</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c24">SSSS</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/>
<a NAME="E19:129"/>
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c6">phi0</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c31">R</font> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a>  &amp; <font color="Maroon" title="c31">R</font> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <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="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/>
<a NAME="E20:129"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">Z4</font></span>: 
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c6">phi0</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <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="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a>  &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c6">phi0</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c30">Tm</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:129"><span class="lab"><font color="Green" title="E59">B5</font></span></a>, <a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/>
<span class="lab"><font color="Green" title="E63">B0</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c6">phi0</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c30">Tm</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c6">phi0</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:129"><span class="lab"><font color="Green" title="E62">Z4</font></span></a>, <a class="txt" href="#E15:129"><span class="lab"><font color="Green" title="E60">B6</font></span></a>, <a class="ref" href="relat_1.html#T165" title="RELAT_1:th.165">RELAT_1:165</a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c4">l2</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c30">Tm</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c6">phi0</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel3.html#E67"><span class="lab"><font color="Green" title="E54">Lm44</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c4">l2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c30">Tm</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c6">phi0</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T83" title="RELAT_1:th.83">RELAT_1:83</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c4">l2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">l2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c30">Tm</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c6">phi0</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T36" title="RELAT_1:th.36">RELAT_1:36</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">l1</font> <a href="fomodel0.html#K20" title="FOMODEL0:func.20">SubstWith</a> <font color="Maroon" title="c4">l2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c6">phi0</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:129"><span class="lab"><font color="Green" title="E62">Z4</font></span></a>, <a class="txt" href="#E16:129"><span class="lab"><font color="Green" title="E61">B8</font></span></a>, <a class="ref" href="relat_1.html#T165" title="RELAT_1:th.165">RELAT_1:165</a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c25">psi0</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel3.html#E66"><span class="lab"><font color="Green" title="E53">Lm41</font></span></a></span>
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="129_5"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:129_5"/>
( <font color="Maroon" title="c26">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c3">S</font> or <font color="Maroon" title="c26">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c3">S</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="129_5_1"><span class="kw">suppose </span></a><a NAME="E1:129_5_1"/><span class="lab"><font color="Green" title="E64">C0</font></span>: 
<font color="Maroon" title="c26">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c3">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Maroon" title="c6">phi0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c4">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c6">phi0</font></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Maroon" title="c6">phi0</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">r2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c25">psi0</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:129"><span class="lab"><font color="Green" title="E63">B0</font></span></a>, <a class="txt" href="#E5:129"><span class="lab"><font color="Green" title="E56">B1</font></span></a>, <a class="txt" href="#E8:129"><span class="lab"><font color="Green" title="E57">B2</font></span></a>, <a class="ref" href="fomodel2.html#T14" title="FOMODEL2:th.14">FOMODEL2:14</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Maroon" title="c25">psi0</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:129_5_1"><span class="lab"><font color="Green" title="E64">C0</font></span></a>, <a class="txt" href="#E5:129"><span class="lab"><font color="Green" title="E56">B1</font></span></a>, <a class="ref" href="fomodel2.html#T14" title="FOMODEL2:th.14">FOMODEL2:14</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:129_5_1"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Maroon" title="c6">phi0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c4">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c6">phi0</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="129_5_2"><span class="kw">suppose </span></a><a NAME="E1:129_5_2"/><span class="lab"><font color="Green" title="E64">C0</font></span>: 
<font color="Maroon" title="c26">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K34" title="FOMODEL2:func.34">TheEqSymbOf</a> <font color="Maroon" title="c3">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Maroon" title="c6">phi0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c4">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c6">phi0</font></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Maroon" title="c6">phi0</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K2" title="FOMODEL2:func.2">-deltaInterpreter</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K34" title="FOMODEL1:func.34">SubTerms</a> <font color="Maroon" title="c6">phi0</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#T14" title="FOMODEL2:th.14">FOMODEL2:14</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Maroon" title="c25">psi0</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:129_5_2"><span class="lab"><font color="Green" title="E64">C0</font></span></a>, <a class="txt" href="#E5:129"><span class="lab"><font color="Green" title="E56">B1</font></span></a>, <a class="txt" href="#E21:129"><span class="lab"><font color="Green" title="E63">B0</font></span></a>, <a class="ref" href="fomodel2.html#T14" title="FOMODEL2:th.14">FOMODEL2:14</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:129_5_2"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <font color="Maroon" title="c6">phi0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c2">u</font>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="fomodel2.html#K14" title="FOMODEL2:func.14">-AtomicEval</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c4">l2</font>) <a href="fomodel3.html#K24" title="FOMODEL3:func.24">-SymbolSubstIn</a> <font color="Maroon" title="c6">phi0</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
