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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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><br/>  for <font color="Olive" title="b2">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> holds   <a href="qc_lang1.html#K15" title="QC_LANG1:func.15">the_pred_symbol_of</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b2">ll</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">P</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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> holds   <a href="qc_lang1.html#K15" title="QC_LANG1:func.15">the_pred_symbol_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b1">ll</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="qc_lang1.html#K15" title="QC_LANG1:func.15">the_pred_symbol_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c3">ll</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font></span><br/>





<a NAME="E1:90"/><span class="lab"><font color="Green" title="E52">A1</font></span>: 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">P</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">ll</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T41" title="FINSEQ_1:th.41">FINSEQ_1:41</a></span>;<br/>
<a NAME="E2:90"/>
<font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c3">ll</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D16" title="QC_LANG1:def.16">QC_LANG1:def 16</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">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="c5">ll9</font> being   <a href="qc_lang1.html#NM7" title="QC_LANG1:NM.7">QC-variable_list</a> of <font color="Maroon" title="c4">k</font>, <font color="Maroon" title="c6">P9</font> being   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c4">k</font><span class="kw"> such that </span><br/><a NAME="E4:90"/><span class="lab"><font color="Green" title="E53">A2</font></span>: 
(  <a href="qc_lang1.html#K15" title="QC_LANG1:func.15">the_pred_symbol_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c3">ll</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">P9</font> &amp; <font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c3">ll</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">P9</font> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <font color="Maroon" title="c5">ll9</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D20" title="QC_LANG1:def.20">QC_LANG1:def 20</a></span>;<br/>
<a NAME="E5:90"/>
( <font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c3">ll</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">P</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">ll</font> &amp; <font color="Maroon" title="c6">P9</font> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <font color="Maroon" title="c5">ll9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c6">P9</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c5">ll9</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#T6" title="QC_LANG1:th.6">QC_LANG1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:90"/>
 <a href="qc_lang1.html#K15" title="QC_LANG1:func.15">the_pred_symbol_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c3">ll</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:90"><span class="lab"><font color="Green" title="E53">A2</font></span></a>, <a class="txt" href="#E1:90"><span class="lab"><font color="Green" title="E52">A1</font></span></a>, <a class="ref" href="finseq_1.html#T41" title="FINSEQ_1:th.41">FINSEQ_1:41</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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