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<span class="kw">set </span><font color="Maroon" title="c2">Sub</font> =  the   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">x</font> =  the   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">B</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K5" title="CQC_LANG:func.5">VERUM</a> <font color="Maroon" title="c1">Al</font></span>)</span>, the   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>, the   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>;<br/>
<a NAME="E1:37_1_1"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
 <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">VERUM</a> <font color="Maroon" title="c1">Al</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"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D14" onmouseover="rs('qc_lang1/D14')" onmouseout="rh()">QC_LANG1:def 14</a></span>;<br/>
<a NAME="E2:37_1_1"/><span class="lab"><font color="Green" title="E28">A2</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>, the   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut1.html#D16" onmouseover="rs('substut1/D16')" onmouseout="rh()">SUBSTUT1:def 16</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">S</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K5" title="CQC_LANG:func.5">VERUM</a> <font color="Maroon" title="c1">Al</font></span>)</span>, the   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1_1"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="substut1.html#D16" onmouseover="rs('substut1/D16')" onmouseout="rh()">SUBSTUT1:def 16</a></span>;<br/>
<a NAME="E4:37_1_1"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K5" title="CQC_LANG:func.5">VERUM</a> <font color="Maroon" title="c1">Al</font></span>)</span>, the   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37_1_1"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="ref" href="qc_lang1.html#D14" onmouseover="rs('qc_lang1/D14')" onmouseout="rh()">QC_LANG1:def 14</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">B</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K5" title="CQC_LANG:func.5">VERUM</a> <font color="Maroon" title="c1">Al</font></span>)</span>, the   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>, the   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font></span>)</span>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K3" title="QC_LANG1:func.3">bound_QC-variables</a> <font color="Maroon" title="c1">Al</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c6">B</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="c6">B</font> is  <a href="sublemma.html#V1" title="SUBLEMMA:attr.1">CQC-WFF-like</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c7">X</font> = <span class="p1"> { <span class="default"> <font color="Olive" title="b1">G</font> where <font color="Olive" title="b1">G</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font> : <font color="Olive" title="b1">G</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a>  is    <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> </span> } </span> ;<br/>
<a NAME="E6:37_1_1"/><span class="lab"><font color="Green" title="E29">A3</font></span>: 
<span class="p1"> { <span class="default"> <font color="Olive" title="b1">G</font> where <font color="Olive" title="b1">G</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font> : <font color="Olive" title="b1">G</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a>  is    <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> </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut1.html#D39" onmouseover="rs('substut1/D39')" onmouseout="rh()">SUBSTUT1:def 39</a></span>;<br/>
<a NAME="E7:37_1_1"/>
<font color="Maroon" title="c5">S</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a>  is    <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>
 
;<br/>
<a NAME="E8:37_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:37_1_1"><span class="lab"><font color="Green" title="E29">A3</font></span></a></span>;<br/>
<a NAME="E9:37_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">B</font> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <font color="Maroon" title="c1">Al</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E10:37_1_1"/>
<font color="Maroon" title="c6">B</font> is  <a href="sublemma.html#V1" title="SUBLEMMA:attr.1">CQC-WFF-like</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"> verum</span><br/>


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