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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:109"/><i><font color="Green" title="E68">A1</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 3
 ;<br/>

<a NAME="E2:109"/><i><font color="Green" title="E69">A2</font></i>: 
2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 
;<br/>
<b>set </b><font color="Maroon" title="c2">n1</font> = <font color="Maroon" title="c1">n</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1;<br/>
<a NAME="E3:109"/><i><font color="Green" title="E70">A3</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2
 
<b>by </b><i><a class="txt" href="asympt_1.html#E1:109"><i><font color="Green" title="E68">A1</font></i></a>, <a class="txt" href="asympt_1.html#E2:109"><i><font color="Green" title="E69">A2</font></i></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">n1</font> = <font color="Maroon" title="c1">n</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1 as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a></i>;<br/>
<a NAME="E5:109"/><i><font color="Green" title="E71">A4</font></i>: 
<font color="Maroon" title="c3">n1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
;<br/>
<a NAME="E6:109"/>
<font color="Maroon" title="c3">n1</font> <a href="newton.html#K12" title="NEWTON:func.12">!</a>  <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2
 
<b>by </b><i><a class="txt" href="asympt_1.html#E3:109"><i><font color="Green" title="E70">A3</font></i></a>, <a class="txt" href="asympt_1.html#E104"><i><font color="Green" title="E64">Lm59</font></i></a>, <a class="ref" href="newton.html#T20" title="NEWTON:th.20">NEWTON:20</a></i>;<br/>
<a NAME="E7:109"/><b>then </b>
<font color="Maroon" title="c3">n1</font> <a href="newton.html#K12" title="NEWTON:func.12">!</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E8:109"/><b>then </b>
<font color="Maroon" title="c1">n</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">n1</font> <a href="newton.html#K12" title="NEWTON:func.12">!</a> </span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c1">n</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 1
 
<b>by </b><i><a class="txt" href="asympt_1.html#E1:109"><i><font color="Green" title="E68">A1</font></i></a>, <a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></i>;<br/>
<b>hence </b><a NAME="E9:109"/>
<font color="Maroon" title="c1">n</font> <a href="newton.html#K12" title="NEWTON:func.12">!</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="txt" href="asympt_1.html#E5:109"><i><font color="Green" title="E71">A4</font></i></a>, <a class="ref" href="newton.html#T21" title="NEWTON:th.21">NEWTON:21</a></i>;<br/>


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