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

<b>let </b><font color="Maroon" title="c1">S</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> ;<br/><b>let </b><font color="Maroon" title="c2">R</font> be  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c1">S</font>;<br/><b>let </b><font color="Maroon" title="c3">BASSIGN</font> be  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="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <font color="Maroon" title="c1">S</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">g</font>, <font color="Maroon" title="c6">h1</font>, <font color="Maroon" title="c7">h2</font> be   <a href="modelc_1.html#NM2" title="MODELC_1:NM.2">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K50" title="MODELC_1:func.50">CTLModel</a> <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font></span>)</span>;<br/>







<b>assume </b><a NAME="E1:172"/><i><font color="Green" title="E130">A1</font></i>: 
for <font color="Olive" title="b1">s</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c6">h1</font> holds <br/><font color="Olive" title="b1">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c7">h2</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c8">s</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font>;<br/>

<b>assume </b><a NAME="E2:172"/><i><font color="Green" title="E131">A2</font></i>: 
<font color="Maroon" title="c8">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K61" title="MODELC_1:func.61">Foax</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">h1</font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="172_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:172_1"/>
( <font color="Maroon" title="c8">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c5">g</font> or <font color="Maroon" title="c8">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K55" title="MODELC_1:func.55">Fax</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">h1</font> )
 </span><b>by </b><i><a class="txt" href="modelc_1.html#E2:172"><i><font color="Green" title="E131">A2</font></i></a>, <a class="ref" href="modelc_1.html#T17" target="_self" title="MODELC_1:th.17">Th17</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="172_1_1"><b>suppose </b></a><a NAME="E1:172_1_1"/>
<font color="Maroon" title="c8">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c5">g</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:172_1_1"/>
<font color="Maroon" title="c8">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K61" title="MODELC_1:func.61">Foax</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c7">h2</font>
 <b>by </b><i><a class="ref" href="modelc_1.html#T17" target="_self" title="MODELC_1:th.17">Th17</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="172_1_2"><b>suppose </b></a><a NAME="E1:172_1_2"/>
<font color="Maroon" title="c8">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K55" title="MODELC_1:func.55">Fax</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">h1</font>
 ;<br/><div class="add"><a NAME="E2:172_1_2"/><b>then </b><i><font color="Green" title="E132">A3</font></i>: 
( <font color="Maroon" title="c8">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c8">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K27" title="MODELC_1:func.27">EX</a> <font color="Maroon" title="c6">h1</font> )
 <b>by </b><i><a class="ref" href="modelc_1.html#T13" target="_self" title="MODELC_1:th.13">Th13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c9">pai</font> being    <a href="modelc_1.html#M1" title="MODELC_1:mode.1">inf_path</a> of <font color="Maroon" title="c2">R</font><b> such that </b><br/><a NAME="E4:172_1_2"/><i><font color="Green" title="E133">A4</font></i>: 
<font color="Maroon" title="c9">pai</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">s</font>
 <b>and </b><br/><a NAME="E5:172_1_2"/><i><font color="Green" title="E134">A5</font></i>: 
<font color="Maroon" title="c9">pai</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> 1 <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c6">h1</font>
 <b>by </b><i><a class="ref" href="modelc_1.html#T14" target="_self" title="MODELC_1:th.14">Th14</a></i>;<br/><a NAME="E6:172_1_2"/>
<font color="Maroon" title="c9">pai</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> 1 <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c7">h2</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:172"><i><font color="Green" title="E130">A1</font></i></a>, <a class="txt" href="modelc_1.html#E5:172_1_2"><i><font color="Green" title="E134">A5</font></i></a></i>;<br/><a NAME="E7:172_1_2"/><b>then </b>
<font color="Maroon" title="c8">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K27" title="MODELC_1:func.27">EX</a> <font color="Maroon" title="c7">h2</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E4:172_1_2"><i><font color="Green" title="E133">A4</font></i></a>, <a class="ref" href="modelc_1.html#T14" target="_self" title="MODELC_1:th.14">Th14</a></i>;<br/><a NAME="E8:172_1_2"/><b>then </b>
<font color="Maroon" title="c8">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K26" title="MODELC_1:func.26">'&amp;'</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K27" title="MODELC_1:func.27">EX</a> <font color="Maroon" title="c7">h2</font></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E2:172_1_2"><i><font color="Green" title="E132">A3</font></i></a>, <a class="ref" href="modelc_1.html#T13" target="_self" title="MODELC_1:th.13">Th13</a></i>;<br/><b>hence </b><a NAME="E9:172_1_2"/>
<font color="Maroon" title="c8">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K61" title="MODELC_1:func.61">Foax</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c7">h2</font>
 <b>by </b><i><a class="ref" href="modelc_1.html#T17" target="_self" title="MODELC_1:th.17">Th17</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
