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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E47">lemgcdi</font></span>: <a NAME="T44"><span class="comment"><font color="firebrick">:: FIELD_14:44</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="int_3.html#NM1" title="INT_3:NM.1">EuclidianRing</a><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b4">g</font> being   <a href="ring_4.html#NM2" title="RING_4:NM.2">a_gcd</a> of <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> holds  <span class="p1"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><font color="Olive" title="b4">g</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span> <a href="ideal_1.html#K7" title="IDEAL_1:func.7">-Ideal</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="field_7.html#K1" title="FIELD_7:func.1">{</a><span class="default"><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></span><a href="field_7.html#K1" title="FIELD_7:func.1">}</a></span> <a href="ideal_1.html#K7" title="IDEAL_1:func.7">-Ideal</a> </div></div>
