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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/>

<b>assume </b><a NAME="E1:1"/><i><font color="Green">E1</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 ;<br/>

<b>assume </b><a NAME="E2:1"/><i><font color="Green">E2</font></i>: 
( not <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; not <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1 )
 ;<br/>

<a NAME="E3:1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="cqc_the1.html#E1:1"><i><font color="Green">E1</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/>
<a NAME="E4:1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>hence </b><a NAME="E5:1"/>
contradiction
 <b>by </b><i><a class="txt" href="cqc_the1.html#E2:1"><i><font color="Green">E2</font></i></a>, <a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/>


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