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<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:76"/><i><font color="Green" title="E43">A1</font></i>: 
<font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>and </b><br/><a NAME="E2:76"/><i><font color="Green" title="E44">A2</font></i>: 
<font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>and </b><br/><a NAME="E3:76"/><i><font color="Green" title="E45">A3</font></i>: 
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K5" title="NAT_D:func.5">lcm</a> <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<a NAME="E4:76"/><i><font color="Green" title="E46">A4</font></i>: 
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K5" title="NAT_D:func.5">lcm</a> <font color="Maroon" title="c2">n</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n</font>
 
<b>by </b><i><a class="ref" href="newton.html#T60" target="_self" title="NEWTON:th.60">Th60</a></i>;<br/>
<a NAME="E5:76"/>
( <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K5" title="NAT_D:func.5">lcm</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K5" title="NAT_D:func.5">lcm</a> <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<b>by </b><i><a class="txt" href="newton.html#E3:76"><i><font color="Green" title="E45">A3</font></i></a></i>;<br/>
<a NAME="E6:76"/><b>then </b>
 ex <font color="Olive" title="b1">r</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Olive" title="b1">r</font>
 
<b>by </b><i><a class="txt" href="newton.html#E4:76"><i><font color="Green" title="E46">A4</font></i></a>, <a class="ref" href="nat_d.html#D3" title="NAT_D:def.3">NAT_D:def 3</a></i>;<br/>
<b>hence </b><a NAME="E7:76"/>
contradiction
 <b>by </b><i><a class="txt" href="newton.html#E1:76"><i><font color="Green" title="E43">A1</font></i></a>, <a class="txt" href="newton.html#E2:76"><i><font color="Green" title="E44">A2</font></i></a>, <a class="ref" href="real_2.html#T122" title="REAL_2:th.122">REAL_2:122</a></i>;<br/>


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