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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>now </b></a><div class="add"><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c1">n</font> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 83 &amp; <font color="Maroon" title="c1">n</font> is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> implies  not <font color="Maroon" title="c1">n</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83 )</span><br/><b>assume </b><a NAME="E1:39_1"/><i><font color="Green" title="E38">A1</font></i>: 
( 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c1">n</font> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 83 &amp; <font color="Maroon" title="c1">n</font> is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c1">n</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83</span><br/><a NAME="E2:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 41</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 ;<br/><a NAME="E3:39_1"/><b>then </b><i><font color="Green" title="E39">A2</font></i>: 
not 2 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <b>by </b><i><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></i>;<br/><a NAME="E4:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 27</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2
 ;<br/><a NAME="E5:39_1"/><b>then </b><i><font color="Green" title="E40">A3</font></i>: 
not 3 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <b>by </b><i><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></i>;<br/><a NAME="E6:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">5 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 16</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 3
 ;<br/><a NAME="E7:39_1"/><b>then </b><i><font color="Green" title="E41">A4</font></i>: 
not 5 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <b>by </b><i><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></i>;<br/><a NAME="E8:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">7 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 11</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 6
 ;<br/><a NAME="E9:39_1"/><b>then </b><i><font color="Green" title="E42">A5</font></i>: 
not 7 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <b>by </b><i><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></i>;<br/><a NAME="E10:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">11 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 7</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 6
 ;<br/><a NAME="E11:39_1"/><b>then </b><i><font color="Green" title="E43">A6</font></i>: 
not 11 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <b>by </b><i><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></i>;<br/><a NAME="E12:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">13 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 6</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 5
 ;<br/><a NAME="E13:39_1"/><b>then </b><i><font color="Green" title="E44">A7</font></i>: 
not 13 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <b>by </b><i><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></i>;<br/><a NAME="E14:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">17 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 4</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 15
 ;<br/><a NAME="E15:39_1"/><b>then </b><i><font color="Green" title="E45">A8</font></i>: 
not 17 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <b>by </b><i><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></i>;<br/><a NAME="E16:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">19 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 4</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 7
 ;<br/><a NAME="E17:39_1"/><b>then </b><i><font color="Green" title="E46">A9</font></i>: 
not 19 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <b>by </b><i><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></i>;<br/><a NAME="E18:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">23 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 3</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 14
 ;<br/><a NAME="E19:39_1"/><b>then </b>
not 23 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <b>by </b><i><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></i>;<br/><b>hence </b><a NAME="E20:39_1"/>
not <font color="Maroon" title="c1">n</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <b>by </b><i><a class="txt" href="#E1:39_1"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="#E3:39_1"><i><font color="Green" title="E39">A2</font></i></a>, <a class="txt" href="#E5:39_1"><i><font color="Green" title="E40">A3</font></i></a>, <a class="txt" href="#E7:39_1"><i><font color="Green" title="E41">A4</font></i></a>, <a class="txt" href="#E9:39_1"><i><font color="Green" title="E42">A5</font></i></a>, <a class="txt" href="#E11:39_1"><i><font color="Green" title="E43">A6</font></i></a>, <a class="txt" href="#E13:39_1"><i><font color="Green" title="E44">A7</font></i></a>, <a class="txt" href="#E15:39_1"><i><font color="Green" title="E45">A8</font></i></a>, <a class="txt" href="#E17:39_1"><i><font color="Green" title="E46">A9</font></i></a>, <a class="txt" href="nat_4.html#E36"><i><font color="Green" title="E34">Lm6</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:39"/>
83 is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>
 <b>by </b><i><a class="ref" href="nat_4.html#T14" target="_self" title="NAT_4:th.14">Th14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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