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<div class="add">

<b>let </b><font color="Maroon" title="c1">H</font> be   <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</a>;<br/><b>let </b><font color="Maroon" title="c2">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="c3">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="c2">S</font>,<font color="Maroon" title="c2">S</font>;<br/><b>let </b><font color="Maroon" title="c4">s</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">S</font>;<br/><b>let </b><font color="Maroon" title="c5">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="c2">S</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c6">kai</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_1.html#K19" title="MODELC_1:func.19">atomic_WFF</a> ,the <a href="modelc_1.html#U6" title="MODELC_1:sel.6">BasicAssign</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="c3">R</font>,<font color="Maroon" title="c5">BASSIGN</font></span>)</span>;<br/>











<a NAME="E1:137"/>
( <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">kai</font> <a href="modelc_1.html#R4" title="MODELC_1:pred.4">|=</a>  <a href="modelc_1.html#K10" title="MODELC_1:func.10">EX</a> <font color="Maroon" title="c1">H</font> iff <font color="Maroon" title="c4">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K24" title="MODELC_1:func.24">Evaluate</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K10" title="MODELC_1:func.10">EX</a> <font color="Maroon" title="c1">H</font></span>)</span>,<font color="Maroon" title="c6">kai</font> )
 
<b>by </b><i><a class="ref" href="modelc_1.html#D60" target="_self" title="MODELC_1:def.60">Def60</a></i>;<br/>
<a NAME="E2:137"/><b>then </b><i><font color="Green" title="E105">A1</font></i>: 
( <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">kai</font> <a href="modelc_1.html#R4" title="MODELC_1:pred.4">|=</a>  <a href="modelc_1.html#K10" title="MODELC_1:func.10">EX</a> <font color="Maroon" title="c1">H</font> iff <font color="Maroon" title="c4">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> <span class="p1">(<span class="default"><a href="modelc_1.html#K24" title="MODELC_1:func.24">Evaluate</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c6">kai</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="modelc_1.html#T7" target="_self" title="MODELC_1:th.7">Th7</a></i>;<br/>
<a NAME="E3:137"/><i><font color="Green" title="E106">A2</font></i>: 
(  ex <font color="Olive" title="b1">pai</font> being   <a href="modelc_1.html#M1" title="MODELC_1:mode.1">inf_path</a> of <font color="Maroon" title="c3">R</font> st <br/>( <font color="Olive" title="b1">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="c4">s</font> &amp; <font color="Olive" title="b1">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>  <a href="modelc_1.html#K24" title="MODELC_1:func.24">Evaluate</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c6">kai</font> ) implies  ex <font color="Olive" title="b1">pai</font> being   <a href="modelc_1.html#M1" title="MODELC_1:mode.1">inf_path</a> of <font color="Maroon" title="c3">R</font> st <br/>( <font color="Olive" title="b1">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="c4">s</font> &amp; <font color="Olive" title="b1">pai</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> 1,<font color="Maroon" title="c6">kai</font> <a href="modelc_1.html#R4" title="MODELC_1:pred.4">|=</a> <font color="Maroon" title="c1">H</font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon" title="c7">pai</font> being    <a href="modelc_1.html#M1" title="MODELC_1:mode.1">inf_path</a> of <font color="Maroon" title="c3">R</font><b> such that </b><a NAME="E2:137_1"/><i><font color="Green" title="E107">A3</font></i>: 
( <font color="Maroon" title="c7">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="c4">s</font> &amp; <font color="Maroon" title="c7">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>  <a href="modelc_1.html#K24" title="MODELC_1:func.24">Evaluate</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c6">kai</font> )
 ;<br/>

<b>take </b>
<font color="Maroon" title="c7">pai</font>
;<br/>

<b>thus </b><a NAME="E3:137_1"/>
( <font color="Maroon" title="c7">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="c4">s</font> &amp; <font color="Maroon" title="c7">pai</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> 1,<font color="Maroon" title="c6">kai</font> <a href="modelc_1.html#R4" title="MODELC_1:pred.4">|=</a> <font color="Maroon" title="c1">H</font> )
 <b>by </b><i><a class="txt" href="modelc_1.html#E2:137_1"><i><font color="Green" title="E107">A3</font></i></a>, <a class="ref" href="modelc_1.html#D60" target="_self" title="MODELC_1:def.60">Def60</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:137"/>
(  ex <font color="Olive" title="b1">pai</font> being   <a href="modelc_1.html#M1" title="MODELC_1:mode.1">inf_path</a> of <font color="Maroon" title="c3">R</font> st <br/>( <font color="Olive" title="b1">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="c4">s</font> &amp; <font color="Olive" title="b1">pai</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> 1,<font color="Maroon" title="c6">kai</font> <a href="modelc_1.html#R4" title="MODELC_1:pred.4">|=</a> <font color="Maroon" title="c1">H</font> ) implies  ex <font color="Olive" title="b1">pai</font> being   <a href="modelc_1.html#M1" title="MODELC_1:mode.1">inf_path</a> of <font color="Maroon" title="c3">R</font> st <br/>( <font color="Olive" title="b1">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="c4">s</font> &amp; <font color="Olive" title="b1">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>  <a href="modelc_1.html#K24" title="MODELC_1:func.24">Evaluate</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c6">kai</font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="137_2"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon" title="c7">pai</font> being    <a href="modelc_1.html#M1" title="MODELC_1:mode.1">inf_path</a> of <font color="Maroon" title="c3">R</font><b> such that </b><a NAME="E2:137_2"/><i><font color="Green" title="E107">A4</font></i>: 
( <font color="Maroon" title="c7">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="c4">s</font> &amp; <font color="Maroon" title="c7">pai</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> 1,<font color="Maroon" title="c6">kai</font> <a href="modelc_1.html#R4" title="MODELC_1:pred.4">|=</a> <font color="Maroon" title="c1">H</font> )
 ;<br/>

<b>take </b>
<font color="Maroon" title="c7">pai</font>
;<br/>

<b>thus </b><a NAME="E3:137_2"/>
( <font color="Maroon" title="c7">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="c4">s</font> &amp; <font color="Maroon" title="c7">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>  <a href="modelc_1.html#K24" title="MODELC_1:func.24">Evaluate</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c6">kai</font> )
 <b>by </b><i><a class="txt" href="modelc_1.html#E2:137_2"><i><font color="Green" title="E107">A4</font></i></a>, <a class="ref" href="modelc_1.html#D60" target="_self" title="MODELC_1:def.60">Def60</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:137"/>
( <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">kai</font> <a href="modelc_1.html#R4" title="MODELC_1:pred.4">|=</a>  <a href="modelc_1.html#K10" title="MODELC_1:func.10">EX</a> <font color="Maroon" title="c1">H</font> iff  ex <font color="Olive" title="b1">pai</font> being   <a href="modelc_1.html#M1" title="MODELC_1:mode.1">inf_path</a> of <font color="Maroon" title="c3">R</font> st <br/>( <font color="Olive" title="b1">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="c4">s</font> &amp; <font color="Olive" title="b1">pai</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> 1,<font color="Maroon" title="c6">kai</font> <a href="modelc_1.html#R4" title="MODELC_1:pred.4">|=</a> <font color="Maroon" title="c1">H</font> ) )
 <b>by </b><i><a class="txt" href="modelc_1.html#E2:137"><i><font color="Green" title="E105">A1</font></i></a>, <a class="txt" href="modelc_1.html#E3:137"><i><font color="Green" title="E106">A2</font></i></a>, <a class="ref" href="modelc_1.html#T14" target="_self" title="MODELC_1:th.14">Th14</a></i>;<br/>


</div>
