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

<b>assume </b><a NAME="E1:114"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3
 ;<br/>

<a NAME="E2:114"/><i><font color="Green">E50</font></i>: 
2 <a href="hidden.html#R1">=</a> 3 <a href="real_1.html#K5">-</a> 1
 
;<br/>
<b>set </b><font color="Maroon">n1</font> = <font color="Maroon">n</font> <a href="real_1.html#K5">-</a> 1;<br/>
<a NAME="E3:114"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">n</font> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2
 
<b>by </b><i>, , <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">n1</font> = <font color="Maroon">n</font> <a href="real_1.html#K5">-</a> 1 as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/>
<a NAME="E5:114"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">n1</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 
;<br/>
<a NAME="E6:114"/>
<font color="Maroon">n1</font> <a href="newton.html#K12">!</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2
 
<b>by </b><i>, , <a class="ref" href="newton.html#T20">NEWTON:20</a></i>;<br/>
<a NAME="E7:114"/><b>then </b>
<font color="Maroon">n1</font> <a href="newton.html#K12">!</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E8:114"/><b>then </b>
<font color="Maroon">n</font> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">n1</font> <a href="newton.html#K12">!</a> </span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">n</font> <a href="nat_1.html#K2">*</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/>
<b>hence </b><a NAME="E9:114"/>
<font color="Maroon">n</font> <a href="newton.html#K12">!</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="ref" href="newton.html#T21">NEWTON:21</a></i>;<br/>


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