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<div><span class="kw">theorem </span><a NAME="T93"><span class="comment"><font color="firebrick">:: GROUP_23:93</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>  <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#V5" title="GROUP_23:attr.5">normal</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>  st <font color="Olive" title="b3">F</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  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="b3">F</font> is   <a href="group_19.html#V2" title="GROUP_19:attr.2">internal</a>   <a href="group_19.html#M1" title="GROUP_19:mode.1">DirectSumComponents</a> of <font color="Olive" title="b1">G</font>,<font color="Olive" title="b2">I</font> )</div></div>
