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<div><span class="kw">theorem </span><a NAME="T65"><span class="comment"><font color="firebrick">:: GROUP_1A:65</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#L1" title="ALGSTR_0:struct.1">addMagma</a> <br/>  for <font color="Olive" title="b2">g</font>, <font color="Olive" title="b3">g1</font>, <font color="Olive" title="b4">g2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">G</font> holds  <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">g</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="ideal_1.html#K11" title="IDEAL_1:func.11">+</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b3">g1</font>,<font color="Olive" title="b4">g2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">g</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">g1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">g</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b4">g2</font></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span></div></div>
