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<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>assume </b><a NAME="E1:128"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="intpro_1.html#V10" target="_self">S4_theory</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> ; <i><font color="Red">:: according to </font></i><a class="ref" href="intpro_1.html#D14" target="_self">INTPRO_1:def 14</a><br/>

<b>thus </b><a NAME="E2:128"/>
( <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> <font color="Maroon">c<sub>1</sub></font> &amp; <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> <font color="Maroon">c<sub>1</sub></font> &amp; <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> <font color="Maroon">c<sub>1</sub></font> &amp; <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> <font color="Maroon">c<sub>1</sub></font> &amp; <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> <font color="Maroon">c<sub>1</sub></font> &amp; <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> <font color="Maroon">c<sub>1</sub></font> &amp; <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> <font color="Maroon">c<sub>1</sub></font> &amp; <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> <font color="Maroon">c<sub>1</sub></font> &amp; <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> <font color="Maroon">c<sub>1</sub></font> &amp; ( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <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> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> ) )
 <b>by </b><i><a class="txt" href="intpro_1.html#E1:128"><i><font color="Green">E93</font></i></a>, <a class="ref" href="intpro_1.html#D22" target="_self">Def22</a></i>;<br/>


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