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<b>let </b><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#K4" title="CQC_LANG:func.4">CQC-WFF</a> ;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:61"/><i><font color="Green" title="E49">A1</font></i>: 
<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>
 <b>and </b><br/><a NAME="E2:61"/><i><font color="Green" title="E50">A2</font></i>: 
<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>
 ;<br/>

<a NAME="E3:61"/>
(  <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font> &amp;  <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c1">p</font> )
 
<b>by </b><i><a class="txt" href="cqc_the3.html#E1:61"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="cqc_the3.html#T50" target="_self" title="CQC_THE3:th.50">Th50</a></i>;<br/>
<a NAME="E4:61"/><b>then </b><i><font color="Green" title="E51">A3</font></i>: 
( <font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a>  &amp; <font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a>  )
 
<b>by </b><i><a class="ref" href="cqc_the1.html#D11" title="CQC_THE1:def.11">CQC_THE1:def 11</a></i>;<br/>
<a NAME="E5:61"/>
(  <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <font color="Maroon" title="c3">r</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c4">s</font> &amp;  <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</a> <font color="Maroon" title="c4">s</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c3">r</font> )
 
<b>by </b><i><a class="txt" href="cqc_the3.html#E2:61"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="cqc_the3.html#T50" target="_self" title="CQC_THE3:th.50">Th50</a></i>;<br/>
<a NAME="E6:61"/><b>then </b>
( <font color="Maroon" title="c3">r</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a>  &amp; <font color="Maroon" title="c4">s</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <font color="Maroon" title="c3">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a>  )
 
<b>by </b><i><a class="ref" href="cqc_the1.html#D11" title="CQC_THE1:def.11">CQC_THE1:def 11</a></i>;<br/>
<a NAME="E7:61"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&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">'&amp;'</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</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">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a>  )
 
<b>by </b><i><a class="txt" href="cqc_the3.html#E4:61"><i><font color="Green" title="E51">A3</font></i></a>, <a class="ref" href="procal_1.html#T56" title="PROCAL_1:th.56">PROCAL_1:56</a></i>;<br/>
<a NAME="E8:61"/><b>then </b>
(  <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</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">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&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">'&amp;'</a> <font color="Maroon" title="c4">s</font></span>)</span> &amp;  <a href="cqc_the1.html#NR5" title="CQC_THE1:NR.5">|-</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">'&amp;'</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</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">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="cqc_the1.html#D11" title="CQC_THE1:def.11">CQC_THE1:def 11</a></i>;<br/>
<b>hence </b><a NAME="E9:61"/>
<font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</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">'&amp;'</a> <font color="Maroon" title="c4">s</font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#T50" target="_self" title="CQC_THE3:th.50">Th50</a></i>;<br/>


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