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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E40">Th32</font></span>: <a NAME="T32"><span class="comment"><font color="firebrick">:: GROUP_17:32</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="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">G</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive" title="b3">H</font> being    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b2">G</font><br/>  for <font color="Olive" title="b4">x</font> being  <font color="Olive">b<sub>1</sub></font> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive">b<sub>2</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b5">x0</font> being  <font color="Olive">b<sub>1</sub></font> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive">b<sub>3</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b4">x</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Olive" title="b5">x0</font> holds <br/> <a href="group_17.html#K1" title="GROUP_17:func.1">Product</a> <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_17.html#K1" title="GROUP_17:func.1">Product</a> <font color="Olive" title="b5">x0</font></div></div>
