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<span class="kw">let </span><font color="Maroon" title="c1">A</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">A</font> holds  <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> <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a> <font color="Olive" title="b2">q</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Olive" title="b1">p</font></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">A</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="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c3">q</font> <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a> <font color="Maroon" title="c3">q</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">p</font></span><br/>





<a NAME="E1:28"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="cqc_the3.html#R4" title="CQC_THE3:pred.4">|-|</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">p</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the3.html#T31" target="_self" onmouseover="rs('cqc_the3/T31')" onmouseout="rh()">Th31</a></span>;<br/>
<a NAME="E2:28"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</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></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="cqc_the3.html#R4" title="CQC_THE3:pred.4">|-|</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the3.html#T31" target="_self" onmouseover="rs('cqc_the3/T31')" onmouseout="rh()">Th31</a></span>;<br/>
<a NAME="E3:28"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</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></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="cqc_the3.html#R4" title="CQC_THE3:pred.4">|-|</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">p</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E24">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:28"/>
<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> <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a> <font color="Maroon" title="c3">q</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the3.html#T29" target="_self" onmouseover="rs('cqc_the3/T29')" onmouseout="rh()">Th29</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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