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<b>let </b><font color="Maroon">R</font> be  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V2">unital</a> <a href="group_1.html#V4">associative</a>  <a href="vectsp_1.html#L1">multLoopStr</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/>



<a NAME="E1:40"/>
<font color="Maroon">Amp</font> is    <a href="gcd_1.html#M1" target="_self">Am</a> of <font color="Maroon">R</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:40"/>
(  <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> &amp; ( for <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>  ex <font color="Olive">z</font> being   <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Amp</font> st <font color="Olive">z</font> <a href="gcd_1.html#R4" target="_self">is_associated_to</a> <font color="Olive">a</font> ) &amp; ( for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Amp</font>  st <font color="Olive">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">y</font> holds <br/><font color="Olive">x</font> <a href="gcd_1.html#NR4" target="_self">is_not_associated_to</a> <font color="Olive">y</font> ) )
 <b>by </b><i>, </i>;<br/>


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