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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E141">Th142</font></span>: <a NAME="T188"><span class="comment"><font color="firebrick">:: GROUP_1A:188</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> holds <br/> (  <a href="group_1a.html#K20" title="GROUP_1A:func.20">Left_Cosets</a> <span class="p1">(<span class="default"><a href="group_1a.html#K12" title="GROUP_1A:func.12">(Omega).</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">G</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="group_1a.html#K21" title="GROUP_1A:func.21">Right_Cosets</a> <span class="p1">(<span class="default"><a href="group_1a.html#K12" title="GROUP_1A:func.12">(Omega).</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">G</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )</div></div>
