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<div><span class="kw">theorem </span><a NAME="T169"><span class="comment"><font color="firebrick">:: GROUP_1A:169</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">H</font> being    <a href="group_1a.html#M1" title="GROUP_1A:mode.1">Subgroup</a> of <font color="Olive" title="b1">G</font> holds <br/> (  <a href="group_1a.html#K13" title="GROUP_1A:func.13">carr</a> <font color="Olive" title="b3">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">H</font> <a href="group_1a.html#K19" title="GROUP_1A:func.19">+</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="b3">H</font> <a href="group_1a.html#K19" title="GROUP_1A:func.19">+</a> <span class="p2">(<span class="default"><a href="group_1a.html#K2" title="GROUP_1A:func.2">-</a> <font color="Olive" title="b2">a</font></span>)</span></span>)</span> &amp;  <a href="group_1a.html#K13" title="GROUP_1A:func.13">carr</a> <font color="Olive" title="b3">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">H</font> <a href="group_1a.html#K19" title="GROUP_1A:func.19">+</a> <span class="p2">(<span class="default"><a href="group_1a.html#K2" title="GROUP_1A:func.2">-</a> <font color="Olive" title="b2">a</font></span>)</span></span>)</span> <a href="ideal_1.html#K11" title="IDEAL_1:func.11">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">H</font> <a href="group_1a.html#K19" title="GROUP_1A:func.19">+</a> <font color="Olive" title="b2">a</font></span>)</span> )</div></div>
