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<b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">q</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">r</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">s</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:64"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">p</font> <a href="cqc_the3.html#R7" target="_self">&lt;==&gt;</a> <font color="Maroon">q</font>
 <b>and </b><br/><a NAME="E2:64"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">r</font> <a href="cqc_the3.html#R7" target="_self">&lt;==&gt;</a> <font color="Maroon">s</font>
 ;<br/>

<a NAME="E3:64"/>
( <font color="Maroon">p</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font> is <a href="cqc_the1.html#V2">valid</a> &amp; <font color="Maroon">q</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">p</font> is <a href="cqc_the1.html#V2">valid</a> )
 
<b>by </b><i>, <a class="ref" href="cqc_the3.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E4:64"/><b>then </b><i><font color="Green">E43</font></i>: 
( <font color="Maroon">p</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a>  &amp; <font color="Maroon">q</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a>  )
 
<b>by </b><i><a class="ref" href="cqc_the1.html#D11">CQC_THE1:def 11</a></i>;<br/>
<a NAME="E5:64"/>
( <font color="Maroon">r</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">s</font> is <a href="cqc_the1.html#V2">valid</a> &amp; <font color="Maroon">s</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">r</font> is <a href="cqc_the1.html#V2">valid</a> )
 
<b>by </b><i><a class="ref" href="cqc_the3.html#T9" target="_self">Th9</a>, <a class="ref" href="cqc_the3.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E6:64"/><b>then </b>
( <font color="Maroon">r</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">s</font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a>  &amp; <font color="Maroon">s</font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">r</font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a>  )
 
<b>by </b><i><a class="ref" href="cqc_the1.html#D11">CQC_THE1:def 11</a></i>;<br/>
<a NAME="E7:64"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">r</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">s</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">s</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">r</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a>  )
 
<b>by </b><i><a class="ref" href="cqc_the3.html#T10" target="_self">Th10</a>, <a class="ref" href="procal_1.html#T57">PROCAL_1:57</a></i>;<br/>
<a NAME="E8:64"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">r</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">s</font></span>)</span> is <a href="cqc_the1.html#V2">valid</a> &amp; <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">s</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">r</font></span>)</span> is <a href="cqc_the1.html#V2">valid</a> )
 
<b>by </b><i><a class="ref" href="cqc_the1.html#D11">CQC_THE1:def 11</a></i>;<br/>
<b>hence </b><a NAME="E9:64"/>
<font color="Maroon">p</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">r</font> <a href="cqc_the3.html#R7" target="_self">&lt;==&gt;</a> <font color="Maroon">q</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">s</font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#D1" target="_self">Def1</a></i>;<br/>


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