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<b>let </b><font color="Maroon">k</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:7"/>
<font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">k</font>
 ;<br/>

<a NAME="E2:7"/><b>then </b>
( <font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> &amp; <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> 1 )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a>, <a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/>
<a NAME="E3:7"/><b>then </b>
<font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> 1
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>
<b>hence </b><a NAME="E4:7"/>
contradiction
 ;<br/>


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