<?xml version="1.0"?>
<div class="add">

<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">u1</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">psi</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="Olive" title="b2">S</font>  st  not <font color="Olive" title="b3">l2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b5">psi</font> holds <br/> for <font color="Olive" title="b6">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Olive" title="b2">S</font> holds  <span class="p1">(<span class="default">(<font color="Olive" title="b4">l1</font>,<font color="Olive" title="b1">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Olive" title="b6">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive" title="b5">psi</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">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Olive" title="b6">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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">psi</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">u1</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">psi</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="Olive" title="b1">S</font>  st  not <font color="Olive" title="b2">l2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b4">psi</font> holds <br/> for <font color="Olive" title="b5">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Olive" title="b1">S</font> holds  <span class="p1">(<span class="default">(<font color="Olive" title="b3">l1</font>,<font color="Maroon" title="c2">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Olive" title="b5">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive" title="b4">psi</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">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Olive" title="b5">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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">psi</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">psi</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="c3">S</font>  st  not <font color="Olive" title="b1">l2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b3">psi</font> holds <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="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c3">S</font> holds  <span class="p1">(<span class="default">(<font color="Olive" title="b2">l1</font>,<font color="Maroon" title="c2">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Olive" title="b4">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive" title="b3">psi</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">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Olive" title="b4">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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">psi</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">psi</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="c3">S</font>  st  not <font color="Maroon" title="c4">l2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">psi</font> holds <br/> for <font color="Olive" title="b2">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c3">S</font> holds  <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Olive" title="b2">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive" title="b1">psi</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">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Olive" title="b2">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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">psi</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">psi</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="c3">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">l2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">psi</font> implies  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="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c3">S</font> holds  <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c6">psi</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">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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">psi</font></span>)</span> )</span><br/>











<span class="kw">set </span><font color="Maroon" title="c7">II</font> = <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c3">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">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="c9">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="c10">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">set </span><font color="Maroon" title="c11">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="c12">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="c13">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="c14">N</font> =  <a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c3">S</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c15">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">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <span class="kw">means </span> for <font color="Olive" title="b1">I</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c3">S</font><br/>  for <font color="Olive" title="b2">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="b3">phi</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="c3">S</font>  st <font color="Olive" title="b3">phi</font> is $1 <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  &amp; <font color="Olive" title="b3">phi</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="Olive" title="b2">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive" title="b3">phi</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="Olive" title="b2">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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="b3">phi</font></span>)</span>;<br/>
<a NAME="E2:130"/><span class="lab"><font color="Green" title="E57">B0</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="130_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c16">I</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</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">  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">phi</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="c3">S</font>  st <font color="Olive" title="b2">phi</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  &amp; <font color="Olive" title="b2">phi</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="Olive" title="b1">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c16">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive" title="b2">phi</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="Olive" title="b1">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c16">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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="b2">phi</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c17">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">phi</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="c3">S</font>  st <font color="Olive" title="b1">phi</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  &amp; <font color="Olive" title="b1">phi</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="c17">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c16">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive" title="b1">phi</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="c17">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c16">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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">phi</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c18">phi</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="c3">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="c18">phi</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  &amp; <font color="Maroon" title="c18">phi</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="c17">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c16">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c18">phi</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="c17">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c16">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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="c18">phi</font></span>)</span> )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c19">I1</font> = (<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c17">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c16">I</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c20">I2</font> = (<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c17">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c16">I</font>;<br/>
<span class="kw">assume </span><a NAME="E1:130_1"/>
<font color="Maroon" title="c18">phi</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c18">phi</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>  or <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c17">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c16">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c18">phi</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="c17">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c16">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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="c18">phi</font></span>)</span> )</span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c21">phi0</font> = <font color="Maroon" title="c18">phi</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">assume </span><a NAME="E3:130_1"/>
<font color="Maroon" title="c18">phi</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="c17">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c16">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c18">phi</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="c17">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c16">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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="c18">phi</font></span>)</span></span><br/>

<a NAME="E4:130_1"/><span class="kw">then </span>
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c17">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c16">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c21">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="c17">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c16">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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="c21">phi0</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel3.html#E68"><span class="lab"><font color="Green" title="E55">Lm45</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:130_1"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c17">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c16">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c18">phi</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="c17">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c16">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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="c18">phi</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>
<a NAME="E3:130"/><span class="lab"><font color="Green" title="E58">B1</font></span>: 
 for <font color="Olive" title="b1">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="130_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c16">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c16">n</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c16">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1] )</span><br/>

<span class="kw">assume </span><a NAME="E1:130_2"/><span class="lab"><font color="Green" title="E59">C1</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c16">n</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c16">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]</span><br/>

<span class="kw">let </span><font color="Maroon" title="c17">I</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</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">  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">phi</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="c3">S</font>  st <font color="Olive" title="b2">phi</font> is <font color="Maroon" title="c16">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  &amp; <font color="Olive" title="b2">phi</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="Olive" title="b1">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive" title="b2">phi</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="Olive" title="b1">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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="b2">phi</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c18">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">phi</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="c3">S</font>  st <font color="Olive" title="b1">phi</font> is <font color="Maroon" title="c16">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  &amp; <font color="Olive" title="b1">phi</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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Olive" title="b1">phi</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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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">phi</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c19">phi</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="c3">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="c19">phi</font> is <font color="Maroon" title="c16">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  &amp; <font color="Maroon" title="c19">phi</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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c19">phi</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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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="c19">phi</font></span>)</span> )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c20">I1</font> = (<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c21">I2</font> = (<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font>;<br/>
<span class="kw">assume </span><a NAME="E2:130_2"/><span class="lab"><font color="Green" title="E60">C0</font></span>: 
( <font color="Maroon" title="c19">phi</font> is <font color="Maroon" title="c16">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  &amp; <font color="Maroon" title="c19">phi</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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c19">phi</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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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="c19">phi</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c22">phii</font> = <font color="Maroon" title="c19">phi</font> as  <font color="Maroon" title="c16">n</font> <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="c3">S</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c23">x</font> = <font color="Maroon" title="c19">phi</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Maroon" title="c15">SSSS</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:130_2"><span class="lab"><font color="Green" title="E60">C0</font></span></a></span>;<br/>
<a NAME="E5:130_2"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c23">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<br/>
<a NAME="E6:130_2"/><span class="kw">then </span>
<font color="Maroon" title="c22">phii</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T60" title="ZFMISC_1:th.60">ZFMISC_1:60</a></span>;<br/>
<a NAME="E7:130_2"/><span class="kw">then </span>
<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="c22">phii</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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>
 
<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="E8:130_2"/><span class="kw">then </span>
 not <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="c22">phii</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="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E9:130_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">C2</font></span>: 
<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="c22">phii</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">l2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c24">psi</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="c22">phii</font> as  <font color="Maroon" title="c16">n</font> <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="c3">S</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c25">phi1</font> =  <a href="fomodel2.html#K40" title="FOMODEL2:func.40">head</a> <font color="Maroon" title="c22">phii</font> as  <font color="Maroon" title="c16">n</font> <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="c3">S</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c26">psi1</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="c25">phi1</font> as  <font color="Maroon" title="c16">n</font> <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="c3">S</font> ;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="130_2_1"><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="E1:130_2_1"/>
( ( <font color="Maroon" title="c19">phi</font> is  <a href="fomodel2.html#V5" title="FOMODEL2:attr.5">exal</a>  &amp;  not <font color="Maroon" title="c19">phi</font> is  <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a>  ) or (  not <font color="Maroon" title="c19">phi</font> is  <a href="fomodel2.html#V5" title="FOMODEL2:attr.5">exal</a>  &amp;  not <font color="Maroon" title="c19">phi</font> is  <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a>  ) or <font color="Maroon" title="c19">phi</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="130_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:130_2_1_1"/>
( <font color="Maroon" title="c19">phi</font> is  <a href="fomodel2.html#V5" title="FOMODEL2:attr.5">exal</a>  &amp;  not <font color="Maroon" title="c19">phi</font> is  <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c19">phi</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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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="c19">phi</font></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c27">phii</font> = <font color="Maroon" title="c22">phii</font> as   non  <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a>  <font color="Maroon" title="c16">n</font> <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="fomodel2.html#V5" title="FOMODEL2:attr.5">exal</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c3">S</font> ;<br/><span class="kw">set </span><font color="Maroon" title="c28">l</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="c27">phii</font>;<br/><span class="kw">set </span><font color="Maroon" title="c29">phi2</font> =  <a href="fomodel2.html#K41" title="FOMODEL2:func.41">tail</a> <font color="Maroon" title="c27">phii</font>;<br/><span class="lab"><font color="Green" title="E62">D2</font></span>: <font color="Maroon" title="c27">phii</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"><span class="p4">(<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="c27">phii</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="c25">phi1</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><a href="fomodel2.html#K41" title="FOMODEL2:func.41">tail</a> <font color="Maroon" title="c27">phii</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#T23" title="FOMODEL2:th.23">FOMODEL2:23</a></span>
<br/>.= 
<span class="p1"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<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="c27">phii</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="c25">phi1</font>

;<br/><span class="kw">then </span><span class="p1">(<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_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c27">phii</font> = 
<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_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="c27">phii</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</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_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">phi1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T36" title="FOMODEL0:th.36">FOMODEL0:36</a></span>
<br/>.= 
<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_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="c27">phii</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c26">psi1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#D23" title="FOMODEL0:def.23">FOMODEL0:def 23</a></span>
;<br/><a NAME="E5:130_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">D1</font></span>: 
<font color="Maroon" title="c24">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="c27">phii</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c26">psi1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#D23" title="FOMODEL0:def.23">FOMODEL0:def 23</a></span>;<br/><a NAME="E6:130_2_1_1"/>
<font color="Maroon" title="c23">x</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"><span class="p4">(<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="c27">phii</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="c25">phi1</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:130_2_1_1"><span class="lab"><font color="Green" title="E62">D2</font></span></a></span>;<br/><a NAME="E7:130_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">D3</font></span>: 
<font color="Maroon" title="c25">phi1</font> is <font color="Maroon" title="c15">SSSS</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T44" title="FOMODEL0:th.44">FOMODEL0:44</a></span>;<br/><a NAME="E8:130_2_1_1"/>
( <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 iff <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c24">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="130_2_1_1_3"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="130_2_1_1_3_1"><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="E1:130_2_1_1_3_1"/>
( <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="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l1</font> or <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="c27">phii</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">l1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="130_2_1_1_3_1_1"><span class="kw">suppose </span></a><a NAME="E1:130_2_1_1_3_1_1"/><span class="lab"><font color="Green" title="E65">E0</font></span>: 
<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="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l1</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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 iff <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c24">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/><div class="add"><a NAME="E2:130_2_1_1_3_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">Z1</font></span>: 
<font color="Maroon" title="c24">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><font color="Maroon" title="c4">l2</font></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="c26">psi1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:130_2_1_1"><span class="lab"><font color="Green" title="E63">D1</font></span></a>, <a class="ref" href="fomodel0.html#T35" title="FOMODEL0:th.35">FOMODEL0:35</a></span>;<br/><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c24">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:130_2_1_1_3_1_1_1"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c24">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c30">u1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">U</font><span class="kw"> such that </span><br/><a NAME="E3:130_2_1_1_3_1_1_1"/><span class="lab"><font color="Green" title="E67">F0</font></span>: 
<span class="p1">(<span class="default">(<span class="p2">(<span class="default"><span class="p3">(<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="c27">phii</font></span>)</span>,<font color="Maroon" title="c30">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c25">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:130_2_1_1"><span class="lab"><font color="Green" title="E62">D2</font></span></a>, <a class="ref" href="fomodel2.html#T19" title="FOMODEL2:th.19">FOMODEL2:19</a></span>;<br/>1 = 
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c30">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c25">phi1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:130_2_1_1_3_1_1_1"><span class="lab"><font color="Green" title="E67">F0</font></span></a>, <a class="txt" href="#E1:130_2_1_1_3_1_1"><span class="lab"><font color="Green" title="E65">E0</font></span></a>, <a class="ref" href="fomodel0.html#T43" title="FOMODEL0:th.43">FOMODEL0:43</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c30">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c26">psi1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:130_2_1_1"><span class="lab"><font color="Green" title="E64">D3</font></span></a>, <a class="txt" href="#E1:130_2"><span class="lab"><font color="Green" title="E59">C1</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c30">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c26">psi1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T43" title="FOMODEL0:th.43">FOMODEL0:43</a></span>
;<br/><span class="kw">hence </span><a NAME="E5:130_2_1_1_3_1_1_1"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c24">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:130_2_1_1_3_1_1"><span class="lab"><font color="Green" title="E66">Z1</font></span></a>, <a class="ref" href="fomodel2.html#T19" title="FOMODEL2:th.19">FOMODEL2:19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E4:130_2_1_1_3_1_1"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c24">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c30">u2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">U</font><span class="kw"> such that </span><br/><a NAME="E6:130_2_1_1_3_1_1"/><span class="lab"><font color="Green" title="E67">F2</font></span>: 
<span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c30">u2</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c26">psi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:130_2_1_1_3_1_1"><span class="lab"><font color="Green" title="E66">Z1</font></span></a>, <a class="ref" href="fomodel2.html#T19" title="FOMODEL2:th.19">FOMODEL2:19</a></span>;<br/>1 = 
<span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c30">u2</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c26">psi1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:130_2_1_1_3_1_1"><span class="lab"><font color="Green" title="E67">F2</font></span></a>, <a class="ref" href="fomodel0.html#T43" title="FOMODEL0:th.43">FOMODEL0:43</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c30">u2</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c25">phi1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:130_2_1_1"><span class="lab"><font color="Green" title="E64">D3</font></span></a>, <a class="txt" href="#E1:130_2"><span class="lab"><font color="Green" title="E59">C1</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="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="c27">phii</font></span>)</span>,<font color="Maroon" title="c30">u2</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c25">phi1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:130_2_1_1_3_1_1"><span class="lab"><font color="Green" title="E65">E0</font></span></a>, <a class="ref" href="fomodel0.html#T43" title="FOMODEL0:th.43">FOMODEL0:43</a></span>
;<br/><span class="kw">hence </span><a NAME="E8:130_2_1_1_3_1_1"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:130_2_1_1"><span class="lab"><font color="Green" title="E62">D2</font></span></a>, <a class="ref" href="fomodel2.html#T19" title="FOMODEL2:th.19">FOMODEL2:19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="130_2_1_1_3_1_2"><span class="kw">suppose </span></a><a NAME="E1:130_2_1_1_3_1_2"/><span class="lab"><font color="Green" title="E65">E0</font></span>: 
<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="c27">phii</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">l1</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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 iff <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c24">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/><div class="add"><a NAME="E2:130_2_1_1_3_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">FF1</font></span>: 
<font color="Maroon" title="c24">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="fomodel2.html#K31" title="FOMODEL2:func.31">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<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="c27">phii</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="c26">psi1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:130_2_1_1"><span class="lab"><font color="Green" title="E63">D1</font></span></a>, <a class="ref" href="fomodel0.html#T35" title="FOMODEL0:th.35">FOMODEL0:35</a></span>;<br/><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c24">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:130_2_1_1_3_1_2_1"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c24">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c30">u1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">U</font><span class="kw"> such that </span><br/><a NAME="E3:130_2_1_1_3_1_2_1"/><span class="lab"><font color="Green" title="E67">F0</font></span>: 
<span class="p1">(<span class="default">(<span class="p2">(<span class="default"><span class="p3">(<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="c27">phii</font></span>)</span>,<font color="Maroon" title="c30">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c25">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:130_2_1_1"><span class="lab"><font color="Green" title="E62">D2</font></span></a>, <a class="ref" href="fomodel2.html#T19" title="FOMODEL2:th.19">FOMODEL2:19</a></span>;<br/>1 = 
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<span class="p3">(<span class="default"><span class="p4">(<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="c27">phii</font></span>)</span>,<font color="Maroon" title="c30">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c25">phi1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:130_2_1_1_3_1_2_1"><span class="lab"><font color="Green" title="E67">F0</font></span></a>, <a class="txt" href="#E1:130_2_1_1_3_1_2"><span class="lab"><font color="Green" title="E65">E0</font></span></a>, <a class="ref" href="fomodel0.html#T43" title="FOMODEL0:th.43">FOMODEL0:43</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<span class="p3">(<span class="default"><span class="p4">(<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="c27">phii</font></span>)</span>,<font color="Maroon" title="c30">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c26">psi1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:130_2"><span class="lab"><font color="Green" title="E59">C1</font></span></a>, <a class="txt" href="#E7:130_2_1_1"><span class="lab"><font color="Green" title="E64">D3</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="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="c27">phii</font></span>)</span>,<font color="Maroon" title="c30">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c26">psi1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:130_2"><span class="lab"><font color="Green" title="E61">C2</font></span></a>, <a class="ref" href="fomodel0.html#T43" title="FOMODEL0:th.43">FOMODEL0:43</a></span>
;<br/><span class="kw">hence </span><a NAME="E5:130_2_1_1_3_1_2_1"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c24">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:130_2_1_1_3_1_2"><span class="lab"><font color="Green" title="E66">FF1</font></span></a>, <a class="ref" href="fomodel2.html#T19" title="FOMODEL2:th.19">FOMODEL2:19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E4:130_2_1_1_3_1_2"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c24">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c30">u2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">U</font><span class="kw"> such that </span><br/><a NAME="E6:130_2_1_1_3_1_2"/><span class="lab"><font color="Green" title="E67">F2</font></span>: 
<span class="p1">(<span class="default">(<span class="p2">(<span class="default"><span class="p3">(<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="c27">phii</font></span>)</span>,<font color="Maroon" title="c30">u2</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c26">psi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:130_2_1_1_3_1_2"><span class="lab"><font color="Green" title="E66">FF1</font></span></a>, <a class="ref" href="fomodel2.html#T19" title="FOMODEL2:th.19">FOMODEL2:19</a></span>;<br/>1 = 
<span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<span class="p3">(<span class="default"><span class="p4">(<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="c27">phii</font></span>)</span>,<font color="Maroon" title="c30">u2</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c26">psi1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:130_2"><span class="lab"><font color="Green" title="E61">C2</font></span></a>, <a class="txt" href="#E6:130_2_1_1_3_1_2"><span class="lab"><font color="Green" title="E67">F2</font></span></a>, <a class="ref" href="fomodel0.html#T43" title="FOMODEL0:th.43">FOMODEL0:43</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<span class="p3">(<span class="default"><span class="p4">(<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="c27">phii</font></span>)</span>,<font color="Maroon" title="c30">u2</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c25">phi1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:130_2"><span class="lab"><font color="Green" title="E59">C1</font></span></a>, <a class="txt" href="#E7:130_2_1_1"><span class="lab"><font color="Green" title="E64">D3</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="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="c27">phii</font></span>)</span>,<font color="Maroon" title="c30">u2</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c25">phi1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:130_2_1_1_3_1_2"><span class="lab"><font color="Green" title="E65">E0</font></span></a>, <a class="ref" href="fomodel0.html#T43" title="FOMODEL0:th.43">FOMODEL0:43</a></span>
;<br/><span class="kw">hence </span><a NAME="E8:130_2_1_1_3_1_2"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:130_2_1_1"><span class="lab"><font color="Green" title="E62">D2</font></span></a>, <a class="ref" href="fomodel2.html#T19" title="FOMODEL2:th.19">FOMODEL2:19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div><a NAME="E9:130_2_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 iff  not <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c24">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T39" title="FOMODEL0:th.39">FOMODEL0:39</a></span>;<br/><span class="kw">hence </span><a NAME="E10:130_2_1_1"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c19">phi</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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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="c19">phi</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T39" title="FOMODEL0:th.39">FOMODEL0:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="130_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:130_2_1_2"/>
(  not <font color="Maroon" title="c19">phi</font> is  <a href="fomodel2.html#V5" title="FOMODEL2:attr.5">exal</a>  &amp;  not <font color="Maroon" title="c19">phi</font> is  <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c19">phi</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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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="c19">phi</font></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c27">phii</font> = <font color="Maroon" title="c22">phii</font> as   non  <a href="fomodel1.html#V15" title="FOMODEL1:attr.15">0wff</a>  <font color="Maroon" title="c16">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>   non  <a href="fomodel2.html#V5" title="FOMODEL2:attr.5">exal</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="c28">phi2</font> =  <a href="fomodel2.html#K42" title="FOMODEL2:func.42">tail</a> <font color="Maroon" title="c27">phii</font> as  <font color="Maroon" title="c16">n</font> <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="c3">S</font> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c29">psi2</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="c28">phi2</font> as  <font color="Maroon" title="c16">n</font> <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="c3">S</font> ;<br/><a NAME="E5:130_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<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="c27">phii</font></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><a NAME="E6:130_2_1_2"/><span class="kw">then </span>
<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="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K1" title="FOMODEL2:func.1">TheNorSymbOf</a> <font color="Maroon" title="c3">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T29" title="FOMODEL0:th.29">FOMODEL0:29</a></span>;<br/><a NAME="E7:130_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">D0</font></span>: 
<font color="Maroon" title="c27">phii</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="c3">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="c25">phi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c28">phi2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#T23" title="FOMODEL2:th.23">FOMODEL2:23</a></span>;<br/><a NAME="E8:130_2_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c25">phi1</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>  &amp; <font color="Maroon" title="c28">phi2</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>  &amp; ( <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies ( <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c25">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c28">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) ) &amp; ( <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c25">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c28">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:130_2"><span class="lab"><font color="Green" title="E60">C0</font></span></a>, <a class="ref" href="fomodel0.html#T44" title="FOMODEL0:th.44">FOMODEL0:44</a>, <a class="ref" href="fomodel2.html#T19" title="FOMODEL2:th.19">FOMODEL2:19</a></span>;<br/><a NAME="E9:130_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">D2</font></span>: 
( <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 iff ( <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c26">psi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c29">psi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:130_2"><span class="lab"><font color="Green" title="E59">C1</font></span></a></span>;<br/><a NAME="E10:130_2_1_2"/><span class="lab"><font color="Green" title="E64">D1</font></span>: 
( <span class="p1">(<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_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c27">phii</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">psi</font> &amp; <span class="p1">(<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_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">phi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">psi1</font> &amp; <span class="p1">(<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_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c28">phi2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">psi2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#D23" title="FOMODEL0:def.23">FOMODEL0:def 23</a></span>;<br/><span class="kw">then </span><font color="Maroon" title="c24">psi</font> = 
<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_2.html#K3" title="FUNCT_2:func.3">.</a> <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="c3">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="c25">phi1</font></span>)</span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</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_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c28">phi2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:130_2_1_2"><span class="lab"><font color="Green" title="E62">D0</font></span></a>, <a class="ref" href="fomodel0.html#T36" title="FOMODEL0:th.36">FOMODEL0:36</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="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_2.html#K3" title="FUNCT_2:func.3">.</a> <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="c3">S</font></span>)</span></span><a href="fomodel2.html#K31" title="FOMODEL2:func.31">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</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="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c25">phi1</font></span>)</span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</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_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c28">phi2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T36" title="FOMODEL0:th.36">FOMODEL0:36</a></span>
<br/>.= 
<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="c3">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="c26">psi1</font></span>)</span> <a href="fomodel2.html#K30" title="FOMODEL2:func.30">^</a> <font color="Maroon" title="c29">psi2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:130_2_1_2"><span class="lab"><font color="Green" title="E64">D1</font></span></a>, <a class="ref" href="fomodel0.html#T35" title="FOMODEL0:th.35">FOMODEL0:35</a></span>
;<br/><a NAME="E12:130_2_1_2"/><span class="kw">then </span>
( <span class="p1">(<span class="default">(<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c24">psi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 iff  not <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c19">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:130_2_1_2"><span class="lab"><font color="Green" title="E63">D2</font></span></a>, <a class="ref" href="fomodel0.html#T39" title="FOMODEL0:th.39">FOMODEL0:39</a>, <a class="ref" href="fomodel2.html#T19" title="FOMODEL2:th.19">FOMODEL2:19</a></span>;<br/><span class="kw">hence </span><a NAME="E13:130_2_1_2"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c19">phi</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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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="c19">phi</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T39" title="FOMODEL0:th.39">FOMODEL0:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="130_2_1_3"><span class="kw">suppose </span></a><a NAME="E1:130_2_1_3"/>
<font color="Maroon" title="c19">phi</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c19">phi</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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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="c19">phi</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:130_2_1_3"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c19">phi</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="c18">u</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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="c19">phi</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:130"><span class="lab"><font color="Green" title="E57">B0</font></span></a>, <a class="txt" href="#E2:130_2"><span class="lab"><font color="Green" title="E60">C0</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<a NAME="E4:130"/><span class="lab"><font color="Green" title="E59">B2</font></span>: 
 for <font color="Olive" title="b1">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">m</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S2" title="NAT_1:sch.2">NAT_1:sch 2</a>(<a class="txt" href="#E2:130"><span class="lab"><font color="Green" title="E57">B0</font></span></a>, <a class="txt" href="#E3:130"><span class="lab"><font color="Green" title="E58">B1</font></span></a>);<br/></span>
<span class="kw">set </span><font color="Maroon" title="c16">m</font> =  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c6">psi</font>;<br/>
<span class="kw">assume </span><a NAME="E5:130"/>
 not <font color="Maroon" title="c4">l2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">psi</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="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c3">S</font> holds  <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c6">psi</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">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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">psi</font></span>)</span></span><br/>

<a NAME="E6:130"/><span class="kw">then </span>
( <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="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">psi</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">psi</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c3">S</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>, <a class="ref" href="zfmisc_1.html#T50" title="ZFMISC_1:th.50">ZFMISC_1:50</a></span>;<br/>
<a NAME="E7:130"/><span class="kw">then </span>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">psi</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T86" title="XBOOLE_1:th.86">XBOOLE_1:86</a></span>;<br/>
<a NAME="E8:130"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">B3</font></span>: 
( <font color="Maroon" title="c6">psi</font> is  <a href="fomodel2.html#K32" title="FOMODEL2:func.32">Depth</a> <font color="Maroon" title="c6">psi</font> <a href="fomodel2.html#V3" title="FOMODEL2:attr.3">-wff</a>  &amp; <font color="Maroon" title="c6">psi</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>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D31" title="FOMODEL2:def.31">FOMODEL2:def 31</a>, <a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c17">I</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</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">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c6">psi</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">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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">psi</font></span>)</span></span><br/>

<span class="kw">thus </span><a NAME="E9:130"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l1</font>,<font color="Maroon" title="c2">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</a> <font color="Maroon" title="c6">psi</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">u1</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <font color="Maroon" title="c17">I</font></span>)</span> <a href="fomodel2.html#K26" title="FOMODEL2:func.26">-TruthEval</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">psi</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:130"><span class="lab"><font color="Green" title="E59">B2</font></span></a>, <a class="txt" href="#E8:130"><span class="lab"><font color="Green" title="E60">B3</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
