<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="intpro_1.html#K1" target="_self">MC-wff</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="intpro_1.html#K1" target="_self">MC-wff</a> ;<br/>







<b>thus </b><a NAME="E1:114"/>
<font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_1"><b>proof </b></a><div class="add">

<a NAME="E1:114_1"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E2:114_1"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T68" target="_self">Th68</a></i>;<br/>
<b>hence </b><a NAME="E3:114_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="intpro_1.html#E1:114_1"><i><font color="Green">E84</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:114"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_2"><b>proof </b></a><div class="add">

<a NAME="E1:114_2"/><i><font color="Green">E84</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E2:114_2"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T68" target="_self">Th68</a></i>;<br/>
<b>hence </b><a NAME="E3:114_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="intpro_1.html#E1:114_2"><i><font color="Green">E84</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:114"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_3"><b>proof </b></a><div class="add">

<a NAME="E1:114_3"/><i><font color="Green">E84</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E2:114_3"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T68" target="_self">Th68</a></i>;<br/>
<b>hence </b><a NAME="E3:114_3"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="intpro_1.html#E1:114_3"><i><font color="Green">E84</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E4:114"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_4"><b>proof </b></a><div class="add">

<a NAME="E1:114_4"/><i><font color="Green">E84</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E2:114_4"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T68" target="_self">Th68</a></i>;<br/>
<b>hence </b><a NAME="E3:114_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="intpro_1.html#E1:114_4"><i><font color="Green">E84</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E5:114"/>
<font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_5"><b>proof </b></a><div class="add">

<a NAME="E1:114_5"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E2:114_5"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T68" target="_self">Th68</a></i>;<br/>
<b>hence </b><a NAME="E3:114_5"/>
<font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="intpro_1.html#E1:114_5"><i><font color="Green">E84</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E6:114"/>
<font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_6"><b>proof </b></a><div class="add">

<a NAME="E1:114_6"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E2:114_6"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T68" target="_self">Th68</a></i>;<br/>
<b>hence </b><a NAME="E3:114_6"/>
<font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="intpro_1.html#E1:114_6"><i><font color="Green">E84</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E7:114"/>
<font color="Maroon">c<sub>3</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_7"><b>proof </b></a><div class="add">

<a NAME="E1:114_7"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E2:114_7"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T68" target="_self">Th68</a></i>;<br/>
<b>hence </b><a NAME="E3:114_7"/>
<font color="Maroon">c<sub>3</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="intpro_1.html#E1:114_7"><i><font color="Green">E84</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E8:114"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_8"><b>proof </b></a><div class="add">

<a NAME="E1:114_8"/><i><font color="Green">E84</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E2:114_8"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T68" target="_self">Th68</a></i>;<br/>
<b>hence </b><a NAME="E3:114_8"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="intpro_1.html#E1:114_8"><i><font color="Green">E84</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E9:114"/>
<a href="intpro_1.html#K2" target="_self">FALSUM</a>  <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_9"><b>proof </b></a><div class="add">

<a NAME="E1:114_9"/><i><font color="Green">E84</font></i>: 
<a href="intpro_1.html#K2" target="_self">FALSUM</a>  <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E2:114_9"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T68" target="_self">Th68</a></i>;<br/>
<b>hence </b><a NAME="E3:114_9"/>
<a href="intpro_1.html#K2" target="_self">FALSUM</a>  <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="intpro_1.html#E1:114_9"><i><font color="Green">E84</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E10:114"/>
<font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K5" target="_self">'or'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <a href="intpro_1.html#K2" target="_self">FALSUM</a> </span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_10"><b>proof </b></a><div class="add">

<a NAME="E1:114_10"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <a href="intpro_1.html#K1" target="_self">MC-wff</a>  st <font color="Olive">b<sub>1</sub></font> is <a href="intpro_1.html#V9" target="_self">CPC_theory</a> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K5" target="_self">'or'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <a href="intpro_1.html#K2" target="_self">FALSUM</a> </span>)</span> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#D19" target="_self">Def19</a></i>;<br/>
<b>hence </b><a NAME="E2:114_10"/>
<font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K5" target="_self">'or'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <a href="intpro_1.html#K2" target="_self">FALSUM</a> </span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K11" target="_self">CnCPC</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="intpro_1.html#D20" target="_self">Def20</a></i>;<br/>


</div><b>end;</b></div>


</div>
