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<div><span class="kw">theorem </span><a NAME="T51"><span class="comment"><font color="firebrick">:: GROUP_23:51</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>, <font color="Olive" title="b3">S</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="b4">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <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> holds <br/> ( <font color="Olive" title="b4">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Olive" title="b3">S</font> iff  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  <span class="p1">(<span class="default"><a href="group_23.html#K12" title="GROUP_23:func.12">proj</a> (<font color="Olive" title="b2">F</font>,<font color="Olive" title="b5">i</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b3">S</font> <a href="group_7.html#K1" title="GROUP_7:func.1">.</a> <font color="Olive" title="b5">i</font> )</div></div>
