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<div><span class="kw">theorem </span><a NAME="T57"><span class="comment"><font color="firebrick">:: GROUP_1A:57</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>, <font color="Olive" title="b3">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   <a href="group_1a.html#K7" title="GROUP_1A:func.7">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="ideal_1.html#K11" title="IDEAL_1:func.11">+</a> <font color="Olive" title="b3">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="group_1a.html#K7" title="GROUP_1A:func.7">-</a> <font color="Olive" title="b3">B</font></span>)</span> <a href="ideal_1.html#K11" title="IDEAL_1:func.11">+</a> <span class="p1">(<span class="default"><a href="group_1a.html#K7" title="GROUP_1A:func.7">-</a> <font color="Olive" title="b2">A</font></span>)</span></div></div>
