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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:77"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>and </b><br/><a NAME="E2:77"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>and </b><br/><a NAME="E3:77"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K6">lcm</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/>

<a NAME="E4:77"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K6">lcm</a> <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="newton.html#T60" target="_self">Th60</a></i>;<br/>
<a NAME="E5:77"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K6">lcm</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K6">lcm</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 
<b>by </b><i><a class="txt" href="newton.html#E3:77"><i><font color="Green">E46</font></i></a></i>;<br/>
<a NAME="E6:77"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 <a href="nat_1.html#K2">*</a> <font color="Olive">b<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="newton.html#E4:77"><i><font color="Green">E47</font></i></a>, <a class="ref" href="nat_1.html#D3">NAT_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E7:77"/>
contradiction
 <b>by </b><i><a class="txt" href="newton.html#E1:77"><i><font color="Green">E44</font></i></a>, <a class="txt" href="newton.html#E2:77"><i><font color="Green">E45</font></i></a>, <a class="ref" href="real_2.html#T122">REAL_2:122</a></i>;<br/>


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