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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 11 &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> 11 )</span><br/><a NAME="E1:30_1"/>
11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 5</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><a NAME="E2:30_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A1</font></span>: 
not 2 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 11
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></span>;<br/><a NAME="E3:30_1"/>
11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 3</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 ;<br/><a NAME="E4:30_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A2</font></span>: 
not 3 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 11
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></span>;<br/><span class="kw">assume </span><a NAME="E5:30_1"/>
( 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="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 11 &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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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> 11</span><br/><span class="kw">hence </span><a NAME="E6:30_1"/>
not <font color="Maroon" title="c1">n</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 11
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30_1"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E4:30_1"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="nat_4.html#E28"><span class="lab"><font color="Green" title="E27">Lm3</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:30"/>
11 is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T14" target="_self" title="NAT_4:th.14">Th14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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