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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:89_1_1_1"/><i><font color="Green">E36</font></i>: 
0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funcop_1.html#K2" target="_self">--&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><a NAME="E2:89_1_1_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funcop_1.html#K2" target="_self">--&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19" target="_self">Th19</a></i>;<br/><b>hence </b><a NAME="E3:89_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="funcop_1.html#E1:89_1_1_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:89_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="funcop_1.html#K2" target="_self">--&gt;</a> <font color="Maroon">c<sub>2</sub></font> is <a href="relat_1.html#V2">non-empty</a>
 <b>by </b><i><a class="ref" href="relat_1.html#D9">RELAT_1:def 9</a></i>;<br/>


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