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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="intpro_1.html#K1" title="INTPRO_1:func.1">MC-wff</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">r</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="intpro_1.html#K1" title="INTPRO_1:func.1">MC-wff</a>  holds <br/> ( <font color="Olive" title="b1">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Olive" title="b3">r</font></span>)</span></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Olive" title="b3">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Olive" title="b2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b1">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Olive" title="b2">q</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b1">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b2">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Olive" title="b3">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Olive" title="b3">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Olive" title="b3">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a>  <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b1">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c4">r</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="intpro_1.html#K1" title="INTPRO_1:func.1">MC-wff</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a>  <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> )</span><br/>







<a NAME="E1:112"/><span class="lab"><font color="Green" title="E84">A1</font></span>: 
 <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T68" target="_self" title="INTPRO_1:th.68">Th68</a></span>;<br/>
<a NAME="E2:112"/>
<font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T1" target="_self" title="INTPRO_1:th.1">Th1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:112"/>
<font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E84">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a>  <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> )</span><br/>

<a NAME="E4:112"/><span class="lab"><font color="Green" title="E85">A2</font></span>: 
 <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T68" target="_self" title="INTPRO_1:th.68">Th68</a></span>;<br/>
<a NAME="E5:112"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T2" target="_self" title="INTPRO_1:th.2">Th2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:112"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:112"><span class="lab"><font color="Green" title="E85">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a>  <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> )</span><br/>

<a NAME="E7:112"/><span class="lab"><font color="Green" title="E86">A3</font></span>: 
 <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T68" target="_self" title="INTPRO_1:th.68">Th68</a></span>;<br/>
<a NAME="E8:112"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T3" target="_self" title="INTPRO_1:th.3">Th3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:112"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:112"><span class="lab"><font color="Green" title="E86">A3</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a>  <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> )</span><br/>

<a NAME="E10:112"/><span class="lab"><font color="Green" title="E87">A4</font></span>: 
 <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T68" target="_self" title="INTPRO_1:th.68">Th68</a></span>;<br/>
<a NAME="E11:112"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T4" target="_self" title="INTPRO_1:th.4">Th4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:112"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:112"><span class="lab"><font color="Green" title="E87">A4</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a>  <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> )</span><br/>

<a NAME="E13:112"/><span class="lab"><font color="Green" title="E88">A5</font></span>: 
 <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T68" target="_self" title="INTPRO_1:th.68">Th68</a></span>;<br/>
<a NAME="E14:112"/>
<font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T5" target="_self" title="INTPRO_1:th.5">Th5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:112"/>
<font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K4" title="INTPRO_1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:112"><span class="lab"><font color="Green" title="E88">A5</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a>  <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> )</span><br/>

<a NAME="E16:112"/><span class="lab"><font color="Green" title="E89">A6</font></span>: 
 <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T68" target="_self" title="INTPRO_1:th.68">Th68</a></span>;<br/>
<a NAME="E17:112"/>
<font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T6" target="_self" title="INTPRO_1:th.6">Th6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E18:112"/>
<font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:112"><span class="lab"><font color="Green" title="E89">A6</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a>  <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> )</span><br/>

<a NAME="E19:112"/><span class="lab"><font color="Green" title="E90">A7</font></span>: 
 <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T68" target="_self" title="INTPRO_1:th.68">Th68</a></span>;<br/>
<a NAME="E20:112"/>
<font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T7" target="_self" title="INTPRO_1:th.7">Th7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E21:112"/>
<font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:112"><span class="lab"><font color="Green" title="E90">A7</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a>  <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> )</span><br/>

<a NAME="E22:112"/><span class="lab"><font color="Green" title="E91">A8</font></span>: 
 <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T68" target="_self" title="INTPRO_1:th.68">Th68</a></span>;<br/>
<a NAME="E23:112"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T8" target="_self" title="INTPRO_1:th.8">Th8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E24:112"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:112"><span class="lab"><font color="Green" title="E91">A8</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a>  <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font> )</span><br/>

<a NAME="E25:112"/><span class="lab"><font color="Green" title="E92">A9</font></span>: 
 <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T68" target="_self" title="INTPRO_1:th.68">Th68</a></span>;<br/>
<a NAME="E26:112"/>
<a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a>  <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K7" title="INTPRO_1:func.7">CnIPC</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#T9" target="_self" title="INTPRO_1:th.9">Th9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E27:112"/>
<a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a>  <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:112"><span class="lab"><font color="Green" title="E92">A9</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font></span><br/>

<a NAME="E28:112"/>
for <font color="Olive" title="b1">T</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="intpro_1.html#K1" title="INTPRO_1:func.1">MC-wff</a>   st <font color="Olive" title="b1">T</font> is  <a href="intpro_1.html#V9" title="INTPRO_1:attr.9">CPC_theory</a>  &amp; <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">T</font> holds <br/><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#D19" target="_self" title="INTPRO_1:def.19">Def19</a></span>;<br/>
<span class="kw">hence </span><a NAME="E29:112"/>
<font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K5" title="INTPRO_1:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="intpro_1.html#K3" title="INTPRO_1:func.3">=&gt;</a> <a href="intpro_1.html#K2" title="INTPRO_1:func.2">FALSUM</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="intpro_1.html#K11" title="INTPRO_1:func.11">CnCPC</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="intpro_1.html#D20" target="_self" title="INTPRO_1:def.20">Def20</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
