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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>





<b>assume </b><a NAME="E1:68"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K8">hcf</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:68"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="int_2.html#K3">gcd</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="wsierp_1.html#E18"><i><font color="Green">Lemma13</font></i></a></i>;<br/>
<a NAME="E3:68"/>
<font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#R2">divides</a> <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="wsierp_1.html#E1:68"><i><font color="Green">E49</font></i></a>, <a class="txt" href="wsierp_1.html#E12"><i><font color="Green">Lemma7</font></i></a></i>;<br/>
<a NAME="E4:68"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#R2">divides</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="wsierp_1.html#E2:68"><i><font color="Green">E50</font></i></a>, <a class="ref" href="wsierp_1.html#T36" target="_self">Th36</a></i>;<br/>
<b>hence </b><a NAME="E5:68"/>
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E12"><i><font color="Green">Lemma7</font></i></a></i>;<br/>


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