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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E36">Th32</font></span>: <a NAME="T32"><span class="comment"><font color="firebrick">:: GROUP_21:32</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">J</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>   <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Olive" title="b1">I</font><br/>  for <font color="Olive" title="b3">F</font> being    <a href="group_21.html#M2" title="GROUP_21:mode.2">Group-Family</a> of <font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font><br/>  for <font color="Olive" title="b4">x</font>, <font color="Olive" title="b5">y</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b4">x</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_21.html#K15" title="GROUP_21:func.15">dsum</a> <font color="Olive" title="b3">F</font> &amp; <font color="Olive" title="b4">x</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_21.html#K15" title="GROUP_21:func.15">dsum</a> <font color="Olive" title="b3">F</font> holds <br/><span class="p1">(<span class="default"><a href="group_21.html#K16" title="GROUP_21:func.16">dprod2prod</a> <font color="Olive" title="b3">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">x</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_7.html#K3" title="GROUP_7:func.3">sum</a> <span class="p1">(<span class="default"><a href="group_21.html#K9" title="GROUP_21:func.9">Union</a> <font color="Olive" title="b3">F</font></span>)</span></div></div>
