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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E57">defGCD</font></span>   defines <a href="ring_4.html#V4" title="RING_4:attr.4">-gcd</a> <a onclick="hs(this)" href="javascript:()">RING_4:def 10 : <br/></a><span> for <font color="Olive" title="b1">L</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a> <br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font>, <font color="Olive" title="b4">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font> holds <br/> ( <font color="Olive" title="b4">z</font> is <font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font> <a href="ring_4.html#V4" title="RING_4:attr.4">-gcd</a>  iff ( <font color="Olive" title="b4">z</font> <a href="gcd_1.html#R1" title="GCD_1:pred.1">divides</a> <font color="Olive" title="b2">x</font> &amp; <font color="Olive" title="b4">z</font> <a href="gcd_1.html#R1" title="GCD_1:pred.1">divides</a> <font color="Olive" title="b3">y</font> &amp; (  for <font color="Olive" title="b5">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font>  st <font color="Olive" title="b5">r</font> <a href="gcd_1.html#R1" title="GCD_1:pred.1">divides</a> <font color="Olive" title="b2">x</font> &amp; <font color="Olive" title="b5">r</font> <a href="gcd_1.html#R1" title="GCD_1:pred.1">divides</a> <font color="Olive" title="b3">y</font> holds <br/><font color="Olive" title="b5">r</font> <a href="gcd_1.html#R1" title="GCD_1:pred.1">divides</a> <font color="Olive" title="b4">z</font> ) ) );<br/></span></div>
