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

<b>let </b><font color="Maroon">X</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">p</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="intpro_1.html#K1" target="_self">MC-wff</a> ;<br/><b>let </b><font color="Maroon">q</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="intpro_1.html#K1" target="_self">MC-wff</a> ;<br/><b>let </b><font color="Maroon">r</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="E1:133"/>
<font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="133_1"><b>proof </b></a><div class="add">

<a NAME="E1:133_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E2:133_1"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T27" target="_self">Th27</a></i>;<br/>
<b>hence </b><a NAME="E3:133_1"/>
<font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T30" target="_self">Th30</a></i>;<br/>


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

<b>thus </b><a NAME="E2:133"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</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">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">q</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="133_2"><b>proof </b></a><div class="add">

<a NAME="E1:133_2"/><i><font color="Green">E28</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</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">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">q</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</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">X</font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E2:133_2"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T27" target="_self">Th27</a></i>;<br/>
<b>hence </b><a NAME="E3:133_2"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</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">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">q</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T30" target="_self">Th30</a></i>;<br/>


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

<b>thus </b><a NAME="E3:133"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="133_3"><b>proof </b></a><div class="add">

<a NAME="E1:133_3"/><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:133_3"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T27" target="_self">Th27</a></i>;<br/>
<b>hence </b><a NAME="E3:133_3"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T30" target="_self">Th30</a></i>;<br/>


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

<b>thus </b><a NAME="E4:133"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="133_4"><b>proof </b></a><div class="add">

<a NAME="E1:133_4"/><i><font color="Green">E30</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:133_4"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T27" target="_self">Th27</a></i>;<br/>
<b>hence </b><a NAME="E3:133_4"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T30" target="_self">Th30</a></i>;<br/>


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

<b>thus </b><a NAME="E5:133"/>
<font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="133_5"><b>proof </b></a><div class="add">

<a NAME="E1:133_5"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">q</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">X</font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E2:133_5"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T27" target="_self">Th27</a></i>;<br/>
<b>hence </b><a NAME="E3:133_5"/>
<font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T30" target="_self">Th30</a></i>;<br/>


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

<b>thus </b><a NAME="E6:133"/>
<font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="133_6"><b>proof </b></a><div class="add">

<a NAME="E1:133_6"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E2:133_6"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T27" target="_self">Th27</a></i>;<br/>
<b>hence </b><a NAME="E3:133_6"/>
<font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T30" target="_self">Th30</a></i>;<br/>


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

<b>thus </b><a NAME="E7:133"/>
<font color="Maroon">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="133_7"><b>proof </b></a><div class="add">

<a NAME="E1:133_7"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E2:133_7"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T27" target="_self">Th27</a></i>;<br/>
<b>hence </b><a NAME="E3:133_7"/>
<font color="Maroon">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T30" target="_self">Th30</a></i>;<br/>


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

<b>thus </b><a NAME="E8:133"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</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">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</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">p</font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="133_8"><b>proof </b></a><div class="add">

<a NAME="E1:133_8"/><i><font color="Green">E35</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</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">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</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">p</font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</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">X</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:133_8"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T27" target="_self">Th27</a></i>;<br/>
<b>hence </b><a NAME="E3:133_8"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</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">q</font> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</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">p</font> <a href="intpro_1.html#K5" target="_self">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T30" target="_self">Th30</a></i>;<br/>


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

<b>thus </b><a NAME="E9:133"/>
<a href="intpro_1.html#K2" target="_self">FALSUM</a>  <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="133_9"><b>proof </b></a><div class="add">

<a NAME="E1:133_9"/><i><font color="Green">E38</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">p</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E2:133_9"/>
 <a href="intpro_1.html#K7" target="_self">CnIPC</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T27" target="_self">Th27</a></i>;<br/>
<b>hence </b><a NAME="E3:133_9"/>
<a href="intpro_1.html#K2" target="_self">FALSUM</a>  <a href="intpro_1.html#K3" target="_self">=&gt;</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="intpro_1.html#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T30" target="_self">Th30</a></i>;<br/>


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

<b>thus </b><a NAME="E10:133"/>
<font color="Maroon">p</font> <a href="intpro_1.html#K5" target="_self">'or'</a> <span class="p1">(<span class="default"><font color="Maroon">p</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#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="133_10"><b>proof </b></a><div class="add">

<a NAME="E1:133_10"/>
for <font color="Olive">T</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">T</font> is <a href="intpro_1.html#V10" target="_self">S4_theory</a> &amp; <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Olive">T</font> holds <br/><font color="Maroon">p</font> <a href="intpro_1.html#K5" target="_self">'or'</a> <span class="p1">(<span class="default"><font color="Maroon">p</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">T</font>
 
<b>by </b><i><a class="ref" href="intpro_1.html#T24" target="_self">Th24</a></i>;<br/>
<b>hence </b><a NAME="E2:133_10"/>
<font color="Maroon">p</font> <a href="intpro_1.html#K5" target="_self">'or'</a> <span class="p1">(<span class="default"><font color="Maroon">p</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#K13" target="_self">CnS4</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="intpro_1.html#T26" target="_self">Th26</a></i>;<br/>


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


</div>
