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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="Red">::  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="qc_lang1.html#NM7" title="QC_LANG1:NM.7">QC-variable_list</a> of <font color="Maroon" title="c1">k</font> holds  <font color="Olive" title="b1">p</font> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <font color="Olive" title="b2">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="Olive" title="b1">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="Olive" title="b2">ll</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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">ll</font> being  <a href="qc_lang1.html#NM7" title="QC_LANG1:NM.7">QC-variable_list</a> of <font color="Maroon" title="c1">k</font> holds  <font color="Maroon" title="c2">p</font> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <font color="Olive" title="b1">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="Olive" title="b1">ll</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">ll</font> be   <a href="qc_lang1.html#NM7" title="QC_LANG1:NM.7">QC-variable_list</a> of <font color="Maroon" title="c1">k</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">p</font> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</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></span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">QCP</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">Q</font> where <font color="Olive" title="b1">Q</font> is   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-pred_symbol</a> :  <a href="qc_lang1.html#K6" title="QC_LANG1:func.6">the_arity_of</a> <font color="Olive" title="b1">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">k</font> </span>}</span> ;<br/>
<a NAME="E1:39"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">Q</font> where <font color="Olive" title="b1">Q</font> is   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-pred_symbol</a> :  <a href="qc_lang1.html#K6" title="QC_LANG1:func.6">the_arity_of</a> <font color="Olive" title="b1">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">k</font> </span>}</span> 
 
;<br/>
<a NAME="E2:39"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A1</font></span>: 
 ex <font color="Olive" title="b1">Q</font> being  <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-pred_symbol</a> st <br/>( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Q</font> &amp;  <a href="qc_lang1.html#K6" title="QC_LANG1:func.6">the_arity_of</a> <font color="Olive" title="b1">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">k</font> )
 
;<br/>
<a NAME="E3:39"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">ll</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D18" title="FINSEQ_1:def.18">FINSEQ_1:def 18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:39"/>
<font color="Maroon" title="c2">p</font> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="qc_lang1.html#D11" target="_self" title="QC_LANG1:def.11">Def11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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