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<span class="kw">let </span><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font>, <font color="Maroon" title="c3">r</font>, <font color="Maroon" title="c4">s</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"> ( <font color="Maroon" title="c1">p</font> <a href="cqc_the3.html#R7" title="CQC_THE3:pred.7">&lt;==&gt;</a> <font color="Maroon" title="c2">q</font> &amp; <font color="Maroon" title="c3">r</font> <a href="cqc_the3.html#R7" title="CQC_THE3:pred.7">&lt;==&gt;</a> <font color="Maroon" title="c4">s</font> implies <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">&lt;=&gt;</a> <font color="Maroon" title="c3">r</font> <a href="cqc_the3.html#R7" title="CQC_THE3:pred.7">&lt;==&gt;</a> <font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">&lt;=&gt;</a> <font color="Maroon" title="c4">s</font> )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:64"/><span class="lab"><font color="Green" title="E50">A1</font></span>: 
<font color="Maroon" title="c1">p</font> <a href="cqc_the3.html#R7" title="CQC_THE3:pred.7">&lt;==&gt;</a> <font color="Maroon" title="c2">q</font>
 <span class="kw">and </span><br/><a NAME="E2:64"/><span class="lab"><font color="Green" title="E51">A2</font></span>: 
<font color="Maroon" title="c3">r</font> <a href="cqc_the3.html#R7" title="CQC_THE3:pred.7">&lt;==&gt;</a> <font color="Maroon" title="c4">s</font>
 ; <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_lang.html#K10" title="CQC_LANG:func.10">&lt;=&gt;</a> <font color="Maroon" title="c3">r</font> <a href="cqc_the3.html#R7" title="CQC_THE3:pred.7">&lt;==&gt;</a> <font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">&lt;=&gt;</a> <font color="Maroon" title="c4">s</font></span><br/>

<a NAME="E3:64"/><span class="lab"><font color="Green" title="E52">A3</font></span>: 
<font color="Maroon" title="c3">r</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c1">p</font> <a href="cqc_the3.html#R7" title="CQC_THE3:pred.7">&lt;==&gt;</a> <font color="Maroon" title="c4">s</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c2">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="txt" href="#E2:64"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="cqc_the3.html#T55" target="_self" title="CQC_THE3:th.55">Th55</a></span>;<br/>
<a NAME="E4:64"/><span class="lab"><font color="Green" title="E53">A4</font></span>: 
<font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">&lt;=&gt;</a> <font color="Maroon" title="c3">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c1">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang2.html#D4" title="QC_LANG2:def.4">QC_LANG2:def 4</a></span>;<br/>
<a NAME="E5:64"/>
<font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c3">r</font> <a href="cqc_the3.html#R7" title="CQC_THE3:pred.7">&lt;==&gt;</a> <font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="txt" href="#E2:64"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="cqc_the3.html#T55" target="_self" title="CQC_THE3:th.55">Th55</a></span>;<br/>
<a NAME="E6:64"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_the3.html#R7" title="CQC_THE3:pred.7">&lt;==&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:64"><span class="lab"><font color="Green" title="E52">A3</font></span></a>, <a class="ref" href="cqc_the3.html#T54" target="_self" title="CQC_THE3:th.54">Th54</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:64"/>
<font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">&lt;=&gt;</a> <font color="Maroon" title="c3">r</font> <a href="cqc_the3.html#R7" title="CQC_THE3:pred.7">&lt;==&gt;</a> <font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">&lt;=&gt;</a> <font color="Maroon" title="c4">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:64"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="ref" href="qc_lang2.html#D4" title="QC_LANG2:def.4">QC_LANG2:def 4</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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