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<span class="kw">let </span><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>  st <font color="Maroon" title="c1">p</font> <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a> <font color="Maroon" title="c2">q</font> holds <br/> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">p</font>) <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a>  <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b2">y</font>,<font color="Maroon" title="c2">q</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a> <font color="Maroon" title="c2">q</font> implies  <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c1">p</font>) <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a>  <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">q</font>) )</span><br/>







<span class="kw">assume </span><a NAME="E1:42"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
<font color="Maroon" title="c1">p</font> <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a> <font color="Maroon" title="c2">q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c1">p</font>) <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a>  <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">q</font>)</span><br/>

<a NAME="E2:42"/><span class="lab"><font color="Green" title="E37">A2</font></span>: 
<font color="Maroon" title="c2">q</font> <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a>  <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">q</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the3.html#T36" target="_self" title="CQC_THE3:th.36">Th36</a></span>;<br/>
<a NAME="E3:42"/>
 <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c1">p</font>) <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a> <font color="Maroon" title="c1">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the3.html#T36" target="_self" title="CQC_THE3:th.36">Th36</a></span>;<br/>
<a NAME="E4:42"/><span class="kw">then </span>
 <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c1">p</font>) <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a> <font color="Maroon" title="c2">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="cqc_the3.html#T28" target="_self" title="CQC_THE3:th.28">Th28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:42"/>
 <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c1">p</font>) <a href="cqc_the3.html#R5" title="CQC_THE3:pred.5">|-|</a>  <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">q</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="ref" href="cqc_the3.html#T28" target="_self" title="CQC_THE3:th.28">Th28</a></span>; <a class="txt" 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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