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<div><span class="kw">theorem </span><a NAME="T54"><span class="comment"><font color="firebrick">:: GROUP_23:54</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">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="b2">F</font> being   <a href="group_19.html#NM1" title="GROUP_19:NM.1">Group-Family</a> of <font color="Olive" title="b1">I</font><br/>  for <font color="Olive" title="b3">F1</font>, <font color="Olive" title="b4">F2</font> being   <a href="group_23.html#V3" title="GROUP_23:attr.3">componentwise_strict</a>  <a href="group_23.html#NM2" title="GROUP_23:NM.2">Subgroup-Family</a> of <font color="Olive" title="b2">F</font>  st (  for <font color="Olive" title="b5">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">I</font> holds   <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <span class="p1">(<span class="default"><a href="group_23.html#K12" title="GROUP_23:func.12">proj</a> (<font color="Olive" title="b3">F1</font>,<font color="Olive" title="b5">i</font>)</span>)</span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <span class="p1">(<span class="default"><a href="group_23.html#K12" title="GROUP_23:func.12">proj</a> (<font color="Olive" title="b4">F2</font>,<font color="Olive" title="b5">i</font>)</span>)</span> ) holds <br/> <a href="group_23.html#K14" title="GROUP_23:func.14">product</a> <font color="Olive" title="b3">F1</font> is   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_23.html#K14" title="GROUP_23:func.14">product</a> <font color="Olive" title="b4">F2</font></div></div>
