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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="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E1:9"/><i><font color="Green">E7</font></i>: 
 <a href="finseq_1.html#K2" target="_self">Seg</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" target="_self">Seg</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" target="_self">Seg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/>

<b>assume </b><a NAME="E2:9"/><i><font color="Green">E8</font></i>: 
not <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E3:9"/><b>then </b>
 <a href="finseq_1.html#K2" target="_self">Seg</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2" target="_self">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="finseq_1.html#E1:9"><i><font color="Green">E7</font></i></a>, <a class="ref" href="finseq_1.html#T9" target="_self">Th9</a></i>;<br/>
<b>hence </b><a NAME="E4:9"/>
contradiction
 <b>by </b><i><a class="txt" href="finseq_1.html#E2:9"><i><font color="Green">E8</font></i></a>, <a class="ref" href="finseq_1.html#T8" target="_self">Th8</a></i>;<br/>


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