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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="modal_1.html#NM5">MP-wff</a>;<br/>



<b>assume </b><a NAME="E1:56"/><i><font color="Green">E40</font></i>: 
 <a href="modal_1.html#K10" target="_self">'not'</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="modal_1.html#K10" target="_self">'not'</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:56"/><i><font color="Green">E41</font></i>: 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">0</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="trees_1.html#K2">elementary_tree</a> 1</span>)</span> <a href="trees_2.html#K9">--&gt;</a> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="modal_1.html#E55"><i><font color="Green">Lemma38</font></i></a></i>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="trees_1.html#K2">elementary_tree</a> 1</span>)</span> <a href="trees_2.html#K9">--&gt;</a> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span></span>)</span> <a href="trees_2.html#K8">with-replacement</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">0</span><a href="finseq_1.html#K12">*&gt;</a></span>,<font color="Maroon">c<sub>1</sub></font> = 
 <a href="modal_1.html#K10" target="_self">'not'</a> <font color="Maroon">c<sub>1</sub></font>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="trees_1.html#K2">elementary_tree</a> 1</span>)</span> <a href="trees_2.html#K9">--&gt;</a> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span></span>)</span> <a href="trees_2.html#K8">with-replacement</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">0</span><a href="finseq_1.html#K12">*&gt;</a></span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="modal_1.html#E1:56"><i><font color="Green">E40</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E4:56"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="modal_1.html#E2:56"><i><font color="Green">E41</font></i></a>, <a class="ref" href="modal_1.html#T16" target="_self">Th16</a></i>;<br/>


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