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<div><span class="kw">theorem </span><a NAME="T252"><span class="comment"><font color="firebrick">:: GROUP_1A:252</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="group_1a.html#NM1" title="GROUP_1A:NM.1">addGroup</a><br/>  for <font color="Olive" title="b2">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b3">A</font>, <font color="Olive" title="b4">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">G</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b3">A</font> <a href="ideal_1.html#K11" title="IDEAL_1:func.11">+</a> <font color="Olive" title="b4">B</font></span>)</span> <a href="group_1a.html#K27" title="GROUP_1A:func.27">*</a> <font color="Olive" title="b2">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">A</font> <a href="group_1a.html#K27" title="GROUP_1A:func.27">*</a> <font color="Olive" title="b2">a</font></span>)</span> <a href="ideal_1.html#K11" title="IDEAL_1:func.11">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">B</font> <a href="group_1a.html#K27" title="GROUP_1A:func.27">*</a> <font color="Olive" title="b2">a</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_1a.html#T235" target="_self" onmouseover="rs('group_1a/T235')" onmouseout="rh()">Th34</a></span>;<br/></div></div>
