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<b>let </b><font color="Maroon" title="c1">f</font>, <font color="Maroon" title="c2">g</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a> ;<br/>



<b>assume </b><a NAME="E1:32"/><i><font color="Green" title="E30">A1</font></i>: 
(  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font> <a href="calcul_1.html#R2" title="CALCUL_1:pred.2">is_Subsequence_of</a>  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">g</font> &amp;  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c2">g</font> &amp;  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font> <a href="calcul_1.html#R10" title="CALCUL_1:pred.10">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c1">f</font> )
 ;<br/>

<b>let </b><font color="Maroon" title="c3">A</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> ; <i><font color="Red">:: according to </font></i><a class="ref" href="calcul_1.html#D15" target="_self" title="CALCUL_1:def.15">CALCUL_1:def 15</a><br/><b>let </b><font color="Maroon" title="c4">J</font> be    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c3">A</font>;<br/><b>let </b><font color="Maroon" title="c5">v</font> be    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c3">A</font>;<br/>





<b>assume </b><a NAME="E2:32"/><i><font color="Green" title="E31">A2</font></i>: 
<font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="calcul_1.html#R6" title="CALCUL_1:pred.6">|=</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">g</font></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="calcul_1.html#D14" target="_self" title="CALCUL_1:def.14">CALCUL_1:def 14</a><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">p</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a> ;<br/><b>assume </b><a NAME="E1:32_1"/><i><font color="Green" title="E32">A3</font></i>: 
<font color="Maroon" title="c6">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font></span>)</span>
 ;<br/><a NAME="E2:32_1"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">g</font></span>)</span>
 <b>by </b><i><a class="txt" href="calcul_1.html#E1:32"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="calcul_1.html#T1" target="_self" title="CALCUL_1:th.1">Th1</a></i>;<br/><b>hence </b><a NAME="E3:32_1"/>
<font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Maroon" title="c6">p</font>
 <b>by </b><i><a class="txt" href="calcul_1.html#E2:32"><i><font color="Green" title="E31">A2</font></i></a>, <a class="txt" href="calcul_1.html#E1:32_1"><i><font color="Green" title="E32">A3</font></i></a>, <a class="ref" href="calcul_1.html#D11" target="_self" title="CALCUL_1:def.11">Def11</a></i>;<br/></div><b>end;</b></div>
<a NAME="E4:32"/><b>then </b>
<font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="calcul_1.html#R6" title="CALCUL_1:pred.6">|=</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#D11" target="_self" title="CALCUL_1:def.11">Def11</a></i>;<br/>
<a NAME="E5:32"/><b>then </b>
<font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="calcul_1.html#R9" title="CALCUL_1:pred.9">|=</a>  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font>
 
<b>by </b><i><a class="ref" href="calcul_1.html#D14" target="_self" title="CALCUL_1:def.14">Def14</a></i>;<br/>
<b>hence </b><a NAME="E6:32"/>
<font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c2">g</font>
 <b>by </b><i><a class="txt" href="calcul_1.html#E1:32"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="calcul_1.html#D15" target="_self" title="CALCUL_1:def.15">Def15</a></i>;<br/>


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