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<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="39_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 83 &amp; <font color="Olive" title="b1">n</font> is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>  holds <br/> not <font color="Olive" title="b1">n</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83</span></a><div class="add"><span class="kw">let </span><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#NK1" title="NUMBERS:NK.1">NAT</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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#K2" title="NAT_1:func.2">*</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/><a NAME="E1:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 41</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ;<br/><a NAME="E2:39_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A1</font></span>: 
 not 2 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" onmouseover="rs('nat_4/T9')" onmouseout="rh()">Th9</a></span>;<br/><a NAME="E3:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 27</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 ;<br/><a NAME="E4:39_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A2</font></span>: 
 not 3 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" onmouseover="rs('nat_4/T9')" onmouseout="rh()">Th9</a></span>;<br/><a NAME="E5:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">13 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 6</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 5
 ;<br/><a NAME="E6:39_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A3</font></span>: 
 not 13 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" onmouseover="rs('nat_4/T9')" onmouseout="rh()">Th9</a></span>;<br/><a NAME="E7:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">11 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 7</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 6
 ;<br/><a NAME="E8:39_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A4</font></span>: 
 not 11 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" onmouseover="rs('nat_4/T9')" onmouseout="rh()">Th9</a></span>;<br/><a NAME="E9:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">19 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 4</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 7
 ;<br/><a NAME="E10:39_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A5</font></span>: 
 not 19 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" onmouseover="rs('nat_4/T9')" onmouseout="rh()">Th9</a></span>;<br/><a NAME="E11:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">17 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 4</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 15
 ;<br/><a NAME="E12:39_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A6</font></span>: 
 not 17 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" onmouseover="rs('nat_4/T9')" onmouseout="rh()">Th9</a></span>;<br/><a NAME="E13:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">23 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 3</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 14
 ;<br/><a NAME="E14:39_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A7</font></span>: 
 not 23 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" onmouseover="rs('nat_4/T9')" onmouseout="rh()">Th9</a></span>;<br/><a NAME="E15:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">7 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 11</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 6
 ;<br/><a NAME="E16:39_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A8</font></span>: 
 not 7 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" onmouseover="rs('nat_4/T9')" onmouseout="rh()">Th9</a></span>;<br/><a NAME="E17:39_1"/>
83 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 16</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3
 ;<br/><a NAME="E18:39_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A9</font></span>: 
 not 5 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 83
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" onmouseover="rs('nat_4/T9')" onmouseout="rh()">Th9</a></span>;<br/><span class="kw">assume </span><a NAME="E19:39_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#K2" title="NAT_1:func.2">*</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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> 83</span><br/><span class="kw">hence </span><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
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39_1"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="txt" href="#E4:39_1"><span class="lab"><font color="Green" title="E38">A2</font></span></a>, <a class="txt" href="#E18:39_1"><span class="lab"><font color="Green" title="E45">A9</font></span></a>, <a class="txt" href="#E16:39_1"><span class="lab"><font color="Green" title="E44">A8</font></span></a>, <a class="txt" href="#E8:39_1"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="txt" href="#E6:39_1"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="txt" href="#E12:39_1"><span class="lab"><font color="Green" title="E42">A6</font></span></a>, <a class="txt" href="#E10:39_1"><span class="lab"><font color="Green" title="E41">A5</font></span></a>, <a class="txt" href="#E14:39_1"><span class="lab"><font color="Green" title="E43">A7</font></span></a>, <a class="txt" href="nat_4.html#E36"><span class="lab"><font color="Green" title="E33">Lm6</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:39"/>
83 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" onmouseover="rs('nat_4/T14')" onmouseout="rh()">Th14</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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