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<div><span class="kw">theorem </span><a NAME="T99"><span class="comment"><font color="firebrick">:: GROUP_23:99</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive" title="b2">I</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">F</font> being   <a href="group_23.html#V6" title="GROUP_23:attr.6">componentwise_strict</a>   <a href="group_20.html#M1" title="GROUP_20:mode.1">Subgroup-Family</a> of <font color="Olive" title="b2">I</font>,<font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b4">Fam</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Olive" title="b1">G</font></span>)</span>  st <font color="Olive" title="b4">Fam</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b3">F</font> holds <br/>( <font color="Olive" title="b1">G</font> <a href="group_23.html#R1" title="GROUP_23:pred.1">is_internal_product_of</a> <font color="Olive" title="b3">F</font> iff <font color="Olive" title="b1">G</font> <a href="group_23.html#R2" title="GROUP_23:pred.2">is_internal_product_of</a> <font color="Olive" title="b4">Fam</font> )</div></div>
