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<span class="kw">set </span><font color="Maroon" title="c3">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="E1:25_1_1"/>
<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="E2:25_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A1</font></span>: 
 for <font color="Olive" title="b1">G</font> being    <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>  st <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> holds <br/><font color="Olive" title="b1">G</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>
 
;<br/>
<a NAME="E3:25_1_1"/>
 <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">Al</font>
 
;<br/>
<a NAME="E4:25_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="substut1.html#K20" title="SUBSTUT1:func.20">Sub_not</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">Al</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sublemma.html#T16" target="_self" onmouseover="rs('sublemma/T16')" onmouseout="rh()">Th16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:25_1_1"/>
 <a href="substut1.html#K20" title="SUBSTUT1:func.20">Sub_not</a> <font color="Maroon" title="c2">S</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <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="#E2:25_1_1"><span class="lab"><font color="Green" title="E16">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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