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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>, <font color="Olive" title="b2">q</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><br/>  for <font color="Olive" title="b3">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font> holds  <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Olive" title="b2">q</font></span>)</span>,<font color="Olive" title="b3">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sublemma.html#K6" title="SUBLEMMA:func.6">CQCSub_&amp;</a> (<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b3">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>,<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</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">  for <font color="Olive" title="b1">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Maroon" title="c1">Al</font> holds  <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span>,<font color="Olive" title="b1">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sublemma.html#K6" title="SUBLEMMA:func.6">CQCSub_&amp;</a> (<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>,<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Olive" title="b1">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">Sub</font> be   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <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"> <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sublemma.html#K6" title="SUBLEMMA:func.6">CQCSub_&amp;</a> (<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>,<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>)</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">S1</font> = <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">S2</font> = <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>;<br/>
<a NAME="E1:27"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
( <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> &amp; <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> )
 
;<br/>
<a NAME="E2:27"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
( <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> <a href="substut2.html#K5" title="SUBSTUT2:func.5">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">Sub</font> &amp; <span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> <a href="substut2.html#K5" title="SUBSTUT2:func.5">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">Sub</font> )
 
;<br/>
<a NAME="E3:27"/><span class="kw">then </span>
 <a href="sublemma.html#K6" title="SUBLEMMA:func.6">CQCSub_&amp;</a> (<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>,<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K21" title="SUBSTUT1:func.21">Sub_&amp;</a> (<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>,<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sublemma.html#D3" onmouseover="rs('sublemma/D3')" onmouseout="rh()">SUBLEMMA:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:27"/>
<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sublemma.html#K6" title="SUBLEMMA:func.6">CQCSub_&amp;</a> (<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>,<span class="p1"><a href="substut2.html#K2" title="SUBSTUT2:func.2">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">Sub</font></span><a href="substut2.html#K2" title="SUBSTUT2:func.2">]</a></span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="substut1.html#D21" onmouseover="rs('substut1/D21')" onmouseout="rh()">SUBSTUT1:def 21</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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