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<span class="kw">let </span><font color="Maroon" title="c1">Al</font> be    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">Al</font>  st <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  holds <br/> ex <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> ex <font color="Olive" title="b3">P</font> being   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-pred_symbol</a> of <font color="Olive" title="b2">k</font>,<font color="Maroon" title="c1">Al</font> ex <font color="Olive" title="b4">ll</font> being   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Olive" title="b2">k</font>,<font color="Maroon" title="c1">Al</font> st <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b4">ll</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">Al</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  implies  ex <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> ex <font color="Olive" title="b2">P</font> being   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-pred_symbol</a> of <font color="Olive" title="b1">k</font>,<font color="Maroon" title="c1">Al</font> ex <font color="Olive" title="b3">ll</font> being   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Olive" title="b1">k</font>,<font color="Maroon" title="c1">Al</font> st <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b3">ll</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:37"/>
<font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> ex <font color="Olive" title="b2">P</font> being   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-pred_symbol</a> of <font color="Olive" title="b1">k</font>,<font color="Maroon" title="c1">Al</font> ex <font color="Olive" title="b3">ll</font> being   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Olive" title="b1">k</font>,<font color="Maroon" title="c1">Al</font> st <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b3">ll</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>, <font color="Maroon" title="c4">P</font> being   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-pred_symbol</a> of <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c1">Al</font>, <font color="Maroon" title="c5">l</font> being   <a href="qc_lang1.html#NM9" title="QC_LANG1:NM.9">QC-variable_list</a> of <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c1">Al</font><span class="kw"> such that </span><br/><a NAME="E3:37"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P</font> <a href="qc_lang1.html#K10" title="QC_LANG1:func.10">!</a> <font color="Maroon" title="c5">l</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D18" onmouseover="rs('qc_lang1/D18')" onmouseout="rh()">QC_LANG1:def 18</a></span>;<br/>
<a NAME="E4:37"/><span class="lab"><font color="Green" title="E22">A2</font></span>: 
<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">j</font></span>)</span> where <font color="Olive" title="b1">j</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">j</font> &amp; <font color="Olive" title="b1">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">l</font> &amp; <font color="Maroon" title="c5">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="qc_lang1.html#K4" title="QC_LANG1:func.4">fixed_QC-variables</a> <font color="Maroon" title="c1">Al</font> ) </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="cqc_lang.html#T7" onmouseover="rs('cqc_lang/T7')" onmouseout="rh()">CQC_LANG:7</a></span>;<br/>
<a NAME="E5:37"/>
<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span> where <font color="Olive" title="b1">i</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">l</font> &amp; <font color="Maroon" title="c5">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="qc_lang1.html#K5" title="QC_LANG1:func.5">free_QC-variables</a> <font color="Maroon" title="c1">Al</font> ) </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="cqc_lang.html#T7" onmouseover="rs('cqc_lang/T7')" onmouseout="rh()">CQC_LANG:7</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">l</font> = <font color="Maroon" title="c5">l</font> as   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c1">Al</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="ref" href="cqc_lang.html#T5" onmouseover="rs('cqc_lang/T5')" onmouseout="rh()">CQC_LANG:5</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c3">k</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">P</font> being   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-pred_symbol</a> of <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c1">Al</font> ex <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="c3">k</font>,<font color="Maroon" title="c1">Al</font> st <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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><br/>

<span class="kw">take </span>
<font color="Maroon" title="c4">P</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <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="c3">k</font>,<font color="Maroon" title="c1">Al</font> st <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Olive" title="b1">ll</font></span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c6">l</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c6">l</font></span><br/>

<span class="kw">thus </span><a NAME="E7:37"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">P</font> <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">!</a> <font color="Maroon" title="c6">l</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E21">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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