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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E27">Th21</font></span>: <a NAME="T21"><span class="comment"><font color="firebrick">:: GROUP_17:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">q</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">F</font> being   <a href="group_7.html#V2" title="GROUP_7:attr.2">Group-like</a>   <a href="group_7.html#V3" title="GROUP_7:attr.3">associative</a>  <a href="group_7.html#NM1" title="GROUP_7:NM.1">multMagma-Family</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b1">q</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span><br/>  for <font color="Olive" title="b3">G</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>  st <font color="Olive" title="b2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">q</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Olive" title="b3">G</font> holds <br/> ex <font color="Olive" title="b4">I</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Olive" title="b3">G</font>,<span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Olive" title="b2">F</font></span>)</span> st <br/>( <font color="Olive" title="b4">I</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  &amp; (  for <font color="Olive" title="b5">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b3">G</font> holds  <font color="Olive" title="b4">I</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">q</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Olive" title="b5">x</font> ) )</div></div>
