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<b>let </b><font color="Maroon">n</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<i><font color="Green">E38</font></i>:  <a href="euclid.html#K16">0.REAL</a> <font color="Maroon">n</font> = 
 <a href="euclid.html#K5">0*</a> <font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="euclid.html#D9">EUCLID:def 9</a></i>
<br/>.= 
<font color="Maroon">n</font> <a href="finseq_2.html#K2">|-&gt;</a> 0
<b>by </b><i><a class="ref" href="euclid.html#D4">EUCLID:def 4</a></i>
;<br/>
<i><font color="Green">E39</font></i>:  <a href="jordan2c.html#K5">1.REAL</a> <font color="Maroon">n</font> = 
 <a href="jordan2c.html#K4">1*</a> <font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="jordan2c.html#D8">JORDAN2C:def 8</a></i>
<br/>.= 
<font color="Maroon">n</font> <a href="finseq_2.html#K2">|-&gt;</a> 1
<b>by </b><i><a class="ref" href="jordan2c.html#D7">JORDAN2C:def 7</a></i>
;<br/>
<a NAME="E3:24"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/>
<a NAME="E4:24"/><b>then </b>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E5:24"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="finseq_2.html#K2">|-&gt;</a> 0</span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="finseq_2.html#K2">|-&gt;</a> 1</span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 1 )
 
<b>by </b><i><a class="ref" href="finseq_2.html#T71">FINSEQ_2:71</a></i>;<br/>
<b>hence </b><a NAME="E6:24"/>
 <a href="euclid.html#K16">0.REAL</a> <font color="Maroon">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="jordan2c.html#K5">1.REAL</a> <font color="Maroon">n</font>
 <b>by </b><i>, </i>;<br/>


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