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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:31"/><i><font color="Green" title="E34">A1</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 ;<br/>

<b>assume </b><a NAME="E2:31"/><i><font color="Green" title="E35">A2</font></i>: 
 <a href="jordan2c.html#K4" title="JORDAN2C:func.4">1*</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</font>
 ;<br/>

<a NAME="E3:31"/><i><font color="Green" title="E36">A3</font></i>: 
 <a href="jordan2c.html#K4" title="JORDAN2C:func.4">1*</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> 1
 
<b>by </b><i><a class="ref" href="jordan2c.html#D7" title="JORDAN2C:def.7">JORDAN2C:def 7</a></i>;<br/>
<a NAME="E4:31"/><i><font color="Green" title="E37">A4</font></i>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="txt" href="euclidlp.html#E1:31"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E5:31"/><i><font color="Green" title="E38">A5</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> 0</span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<b>by </b><i><a class="txt" href="euclidlp.html#E4:31"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>;<br/>
<a NAME="E6:31"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> 1</span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="txt" href="euclidlp.html#E4:31"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>;<br/>
<b>hence </b><a NAME="E7:31"/>
contradiction
 <b>by </b><i><a class="txt" href="euclidlp.html#E2:31"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="euclidlp.html#E3:31"><i><font color="Green" title="E36">A3</font></i></a>, <a class="txt" href="euclidlp.html#E5:31"><i><font color="Green" title="E38">A5</font></i></a></i>;<br/>


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