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<b>let </b><font color="Maroon" title="c1">j</font>, <font color="Maroon" title="c2">l</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</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">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">l</font> &amp; <font color="Maroon" title="c1">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <font color="Maroon" title="c1">j</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">l</font> <a href="newton.html#K12" title="NEWTON:func.12">!</a>  )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:59"/><i><font color="Green" title="E39">A1</font></i>: 
<font color="Maroon" title="c1">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">l</font>
 <b>and </b><br/><a NAME="E2:59"/><i><font color="Green" title="E40">A2</font></i>: 
<font color="Maroon" title="c1">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</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">j</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">l</font> <a href="newton.html#K12" title="NEWTON:func.12">!</a> </span><br/>

<b>consider </b><font color="Maroon" title="c3">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E4:59"/><i><font color="Green" title="E41">A3</font></i>: 
<font color="Maroon" title="c2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">k</font>
 <b>by </b><i><a class="txt" href="#E1:59"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="nat_1.html#T10" title="NAT_1:th.10">NAT_1:10</a></i>;<br/>
<b>thus </b><a NAME="E5:59"/>
<font color="Maroon" title="c1">j</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">l</font> <a href="newton.html#K12" title="NEWTON:func.12">!</a> 
 <b>by </b><i><a class="txt" href="#E2:59"><i><font color="Green" title="E40">A2</font></i></a>, <a class="txt" href="#E4:59"><i><font color="Green" title="E41">A3</font></i></a>, <a class="ref" href="newton.html#T53" target="_self" title="NEWTON:th.53">Th53</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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