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<b>consider </b><font color="Maroon" title="c2">k</font> being    <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> , <font color="Maroon" title="c3">P</font> being   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c2">k</font>, <font color="Maroon" title="c4">ll</font> being    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-variable_list</a> of <font color="Maroon" title="c2">k</font>, <font color="Maroon" title="c5">e</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K1" title="SUBSTUT1:func.1">vSUB</a> <b> such that </b><br/><a NAME="E2:52_1_1"/><i><font color="Green" title="E28">A2</font></i>: 
<font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K17" title="SUBSTUT1:func.17">Sub_P</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">ll</font>,<font color="Maroon" title="c5">e</font>
 <b>by </b><i><a class="txt" href="#E1:52"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="substut1.html#D25" target="_self" title="SUBSTUT1:def.25">Def25</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">ll</font> = <font color="Maroon" title="c4">ll</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-variables</a>  ;<br/>
<b>take </b>
<font color="Maroon" title="c6">ll</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">k</font> being   <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>  ex <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="Olive" title="b1">k</font> ex <font color="Olive" title="b3">ll</font> being   <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-variable_list</a> of <font color="Olive" title="b1">k</font> ex <font color="Olive" title="b4">e</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K1" title="SUBSTUT1:func.1">vSUB</a>  st <br/>( <font color="Maroon" title="c6">ll</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">ll</font> &amp; <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K17" title="SUBSTUT1:func.17">Sub_P</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">ll</font>,<font color="Olive" title="b4">e</font> )</span><br/>

<b>thus </b><a NAME="E4:52_1_1"/>
 ex <font color="Olive" title="b1">k</font> being   <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>  ex <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="Olive" title="b1">k</font> ex <font color="Olive" title="b3">ll</font> being   <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-variable_list</a> of <font color="Olive" title="b1">k</font> ex <font color="Olive" title="b4">e</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K1" title="SUBSTUT1:func.1">vSUB</a>  st <br/>( <font color="Maroon" title="c6">ll</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">ll</font> &amp; <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K17" title="SUBSTUT1:func.17">Sub_P</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">ll</font>,<font color="Olive" title="b4">e</font> )
 <b>by </b><i><a class="txt" href="#E2:52_1_1"><i><font color="Green" title="E28">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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