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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="calcul_2.html#K2" target="_self">seq</a> <font color="Maroon">c<sub>1</sub></font>,0;<br/><b>assume </b><a NAME="E2:4_1"/><i><font color="Green">E3</font></i>: 
 <a href="calcul_2.html#K2" target="_self">seq</a> <font color="Maroon">c<sub>1</sub></font>,0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/><a NAME="E4:4_1"/>
( 1 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="calcul_2.html#E2:4_1"><i><font color="Green">E3</font></i></a>, <a class="ref" href="calcul_2.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E5:4_1"/>
contradiction
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/></div>
<b>end;</b></div>


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