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<b>let </b><font color="Maroon">R</font> be   <a href="gcd_1.html#NM3">gcdDomain</a>;<br/><b>let </b><font color="Maroon">Amp</font> be    <a href="gcd_1.html#M2" target="_self">AmpleSet</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>;<br/>





<a NAME="E1:59"/><i><font color="Green">E20</font></i>: 
 <a href="group_1.html#K2">1.</a> <font color="Maroon">R</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Amp</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:59"/>
<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R</font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D19">VECTSP_1:def 19</a></i>;<br/>
<a NAME="E3:59"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="group_1.html#K2">1.</a> <font color="Maroon">R</font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:59"/>
for <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>  st <font color="Olive">z</font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">A</font> &amp; <font color="Olive">z</font> <a href="gcd_1.html#R2" target="_self">divides</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">R</font> holds <br/><font color="Olive">z</font> <a href="gcd_1.html#R2" target="_self">divides</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">R</font>
 
;<br/>
<a NAME="E5:59"/><b>then </b>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">A</font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R</font></span>)</span>,<font color="Maroon">Amp</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">R</font>
 
<b>by </b><i>, <a class="ref" href="gcd_1.html#T3" target="_self">Th3</a>, <a class="ref" href="gcd_1.html#D2" target="_self">Def2</a></i>;<br/>
<b>hence </b><a NAME="E6:59"/>
(  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">A</font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R</font></span>)</span>,<font color="Maroon">Amp</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">R</font> &amp;  <a href="gcd_1.html#K5" target="_self">gcd</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">R</font></span>)</span>,<font color="Maroon">A</font>,<font color="Maroon">Amp</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">R</font> )
 <b>by </b><i><a class="ref" href="gcd_1.html#D4" target="_self">Def4</a></i>;<br/>


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