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

<b>let </b><font color="Maroon" title="c1">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">ll</font> being  <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c1">k</font><br/> for <font color="Olive" title="b2">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c1">k</font> holds   <a href="cqc_sim1.html#K13" title="CQC_SIM1:func.13">SepVar</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Olive" title="b1">ll</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Olive" title="b1">ll</font></span><br/><b>let </b><font color="Maroon" title="c2">ll</font> be   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c1">k</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c1">k</font> holds   <a href="cqc_sim1.html#K13" title="CQC_SIM1:func.13">SepVar</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c2">ll</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c2">ll</font></span><br/><b>let </b><font color="Maroon" title="c3">P</font> be   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c1">k</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="cqc_sim1.html#K13" title="CQC_SIM1:func.13">SepVar</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c2">ll</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c2">ll</font></span><br/>





<a NAME="E1:47"/>
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">ll</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a>  &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">ll</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">ll</font> )
 
<b>by </b><i><a class="ref" href="cqc_lang.html#D5" title="CQC_LANG:def.5">CQC_LANG:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">lf</font> = <font color="Maroon" title="c2">ll</font> as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a>  <b>by </b><i><a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<br/>
<a NAME="E3:47"/><i><font color="Green" title="E26">A1</font></i>: 
<span class="p1">(<span class="default"><a href="cqc_sim1.html#K12" title="CQC_SIM1:func.12">id</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">lf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ll</font>
 
<b>by </b><i><a class="ref" href="partfun1.html#T37" title="PARTFUN1:th.37">PARTFUN1:37</a></i>;<br/>
<b>thus </b> <a href="cqc_sim1.html#K13" title="CQC_SIM1:func.13">SepVar</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c2">ll</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="cqc_sim1.html#K5" title="CQC_SIM1:func.5">ATOMIC</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c2">ll</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><a href="cqc_sim1.html#K11" title="CQC_SIM1:func.11">index</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c2">ll</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="cqc_sim1.html#K12" title="CQC_SIM1:func.12">id</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span>
<b>by </b><i><a class="ref" href="cqc_sim1.html#D6" target="_self" title="CQC_SIM1:def.6">Def6</a></i>
<br/>.= 
<font color="Maroon" title="c3">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Maroon" title="c2">ll</font>
<b>by </b><i><a class="txt" href="cqc_sim1.html#E3:47"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="cqc_sim1.html#D4" target="_self" title="CQC_SIM1:def.4">Def4</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
