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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#K9" title="CQC_LANG:func.9">'or'</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#K9" title="CQC_LANG:func.9">'or'</a> <font color="Maroon" title="c4">s</font> )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:63"/><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="E2:63"/><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#K9" title="CQC_LANG:func.9">'or'</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#K9" title="CQC_LANG:func.9">'or'</a> <font color="Maroon" title="c4">s</font></span><br/>

<a NAME="E3:63"/>
<font color="Maroon" title="c4">s</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c3">r</font> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="cqc_the3.html#T50" target="_self" title="CQC_THE3:th.50">Th50</a></span>;<br/>
<a NAME="E4:63"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A3</font></span>: 
<font color="Maroon" title="c4">s</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the1.html#D10" title="CQC_THE1:def.10">CQC_THE1:def 10</a></span>;<br/>
<a NAME="E5:63"/>
<font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c1">p</font> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cqc_the3.html#T50" target="_self" title="CQC_THE3:th.50">Th50</a></span>;<br/>
<a NAME="E6:63"/><span class="kw">then </span>
<font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the1.html#D10" title="CQC_THE1:def.10">CQC_THE1:def 10</a></span>;<br/>
<a NAME="E7:63"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">'or'</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">'or'</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:63"><span class="lab"><font color="Green" title="E52">A3</font></span></a>, <a class="ref" href="procal_1.html#T57" title="PROCAL_1:th.57">PROCAL_1:57</a></span>;<br/>
<a NAME="E8:63"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A4</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">'or'</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">'or'</a> <font color="Maroon" title="c3">r</font></span>)</span> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the1.html#D10" title="CQC_THE1:def.10">CQC_THE1:def 10</a></span>;<br/>
<a NAME="E9:63"/>
<font color="Maroon" title="c3">r</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c4">s</font> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="cqc_the3.html#T50" target="_self" title="CQC_THE3:th.50">Th50</a></span>;<br/>
<a NAME="E10:63"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A5</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="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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the1.html#D10" title="CQC_THE1:def.10">CQC_THE1:def 10</a></span>;<br/>
<a NAME="E11:63"/>
<font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c2">q</font> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="cqc_the3.html#T50" target="_self" title="CQC_THE3:th.50">Th50</a></span>;<br/>
<a NAME="E12:63"/><span class="kw">then </span>
<font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the1.html#D10" title="CQC_THE1:def.10">CQC_THE1:def 10</a></span>;<br/>
<a NAME="E13:63"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">'or'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">'or'</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:63"><span class="lab"><font color="Green" title="E54">A5</font></span></a>, <a class="ref" href="procal_1.html#T57" title="PROCAL_1:th.57">PROCAL_1:57</a></span>;<br/>
<a NAME="E14:63"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">'or'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">'or'</a> <font color="Maroon" title="c4">s</font></span>)</span> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the1.html#D10" title="CQC_THE1:def.10">CQC_THE1:def 10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:63"/>
<font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">'or'</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#K9" title="CQC_LANG:func.9">'or'</a> <font color="Maroon" title="c4">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:63"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="ref" href="cqc_the3.html#T50" target="_self" title="CQC_THE3:th.50">Th50</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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