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<b>let </b><font color="Maroon" title="c4">z1</font>, <font color="Maroon" title="c5">z2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>;<br/>

<b>assume </b><a NAME="E1:42_1_2"/><i><font color="Green" title="E30">A2</font></i>: 
( <font color="Maroon" title="c4">z1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Amp</font> &amp; <font color="Maroon" title="c4">z1</font> <a href="gcd_1.html#R4" title="GCD_1:pred.4">is_associated_to</a> <font color="Maroon" title="c3">x</font> &amp; <font color="Maroon" title="c5">z2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Amp</font> &amp; <font color="Maroon" title="c5">z2</font> <a href="gcd_1.html#R4" title="GCD_1:pred.4">is_associated_to</a> <font color="Maroon" title="c3">x</font> )
 ;<br/>

<a NAME="E2:42_1_2"/><b>then </b>
<font color="Maroon" title="c4">z1</font> <a href="gcd_1.html#R4" title="GCD_1:pred.4">is_associated_to</a> <font color="Maroon" title="c5">z2</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#T4" target="_self" title="GCD_1:th.4">Th4</a></i>;<br/>
<b>hence </b><a NAME="E3:42_1_2"/>
<font color="Maroon" title="c4">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">z2</font>
 <b>by </b><i><a class="txt" href="gcd_1.html#E1:42_1_2"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="gcd_1.html#T22" target="_self" title="GCD_1:th.22">Th22</a></i>;<br/>


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