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<b>let </b><font color="Maroon" title="c1">a</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</font> being  <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>  st <font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">p</font> holds <br/><font color="Maroon" title="c1">a</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/><b>let </b><font color="Maroon" title="c2">p</font> be   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p</font> implies <font color="Maroon" title="c1">a</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:56"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 <b>and </b><br/><a NAME="E2:56"/><i><font color="Green" title="E27">A2</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">a</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/>

<a NAME="E3:56"/>
<font color="Maroon" title="c1">a</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="newton.html#T9" title="NEWTON:th.9">NEWTON:9</a></i>;<br/>
<a NAME="E4:56"/><b>then </b><i><font color="Green" title="E28">A3</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="ref" href="nat_d.html#T6" title="NAT_D:th.6">NAT_D:6</a></i>;<br/>
<a NAME="E5:56"/>
<font color="Maroon" title="c1">a</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font>
 
<b>by </b><i><a class="ref" href="newton.html#T10" title="NEWTON:th.10">NEWTON:10</a></i>;<br/>
<a NAME="E6:56"/><b>then </b>
not <font color="Maroon" title="c1">a</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="txt" href="nat_3.html#E1:56"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="nat_3.html#E2:56"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="int_2.html#D5" title="INT_2:def.5">INT_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E7:56"/>
<font color="Maroon" title="c1">a</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="nat_3.html#E1:56"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="nat_3.html#E4:56"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="nat_3.html#D7" target="_self" title="NAT_3:def.7">Def7</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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