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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="modal_1.html#NM1">MP-variable</a>;<br/>

<a NAME="E1:75"/><i><font color="Green">E58</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="modal_1.html#K16" target="_self">@</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T14">FUNCOP_1:14</a></i>;<br/>
<a NAME="E2:75"/><i><font color="Green">E59</font></i>: 
 <a href="relat_1.html#K2">rng</a> <a href="modal_1.html#K17" target="_self">VERUM</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T14">FUNCOP_1:14</a></i>;<br/>
<b>assume </b><a NAME="E3:75"/>
not  <a href="modal_1.html#K17" target="_self">VERUM</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="modal_1.html#K16" target="_self">@</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E4:75"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="txt" href="modal_1.html#E1:75"><i><font color="Green">E58</font></i></a>, <a class="txt" href="modal_1.html#E2:75"><i><font color="Green">E59</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:75"/>
contradiction
 <b>by </b><i><a class="txt" href="modal_1.html#E76"><i><font color="Green">Lemma56</font></i></a>, <a class="ref" href="modal_1.html#T31" target="_self">Th31</a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>


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