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<div><span class="kw">theorem </span><a NAME="T32"><span class="comment"><font color="firebrick">:: MEASURE9:32</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="simplex0.html#NV1" title="SIMPLEX0:NV.1">with_empty_element</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">F</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Olive" title="b1">X</font>  ex <font color="Olive" title="b3">G</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<font color="Olive" title="b1">X</font> st <br/>( (  for <font color="Olive" title="b4">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Olive" title="b2">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">G</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b4">i</font> ) &amp;  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Olive" title="b2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Olive" title="b3">G</font> )</div></div>
