<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">R</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="group_1.html#V2" title="GROUP_1:attr.2">unital</a> <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a>  <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">multLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">Amp</font> be    <a href="gcd_1.html#M2" title="GCD_1:mode.2">AmpleSet</a> of <font color="Maroon" title="c1">R</font>;<br/>



<a NAME="E1:40"/>
<font color="Maroon" title="c2">Amp</font> is    <a href="gcd_1.html#M1" title="GCD_1:mode.1">Am</a> of <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D8" target="_self" title="GCD_1:def.8">Def8</a></i>;<br/>
<b>hence </b><a NAME="E2:40"/>
(  <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Amp</font> &amp; ( for <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>  ex <font color="Olive" title="b2">z</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">Amp</font> st <font color="Olive" title="b2">z</font> <a href="gcd_1.html#R4" title="GCD_1:pred.4">is_associated_to</a> <font color="Olive" title="b1">a</font> ) &amp; ( for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">Amp</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">y</font> holds <br/><font color="Olive" title="b1">x</font> <a href="gcd_1.html#NR4" title="GCD_1:NR.4">is_not_associated_to</a> <font color="Olive" title="b2">y</font> ) )
 <b>by </b><i><a class="ref" href="gcd_1.html#D7" target="_self" title="GCD_1:def.7">Def7</a>, <a class="ref" href="gcd_1.html#D8" target="_self" title="GCD_1:def.8">Def8</a></i>;<br/>


</div>
