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<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">X</font>, <a href="supinf_1.html#K3">REAL</a> ;<br/>





<b>assume </b><a NAME="E1:78"/>
<font color="Maroon">f</font> <a href="mesfunc6.html#R2" target="_self">is_simple_func_in</a> <font color="Maroon">S</font>
 ;<br/>

<a NAME="E2:78"/><b>then </b>
 ex <font color="Olive">F</font> being  <a href="mesfunc2.html#NM1">Finite_Sep_Sequence</a> of <font color="Maroon">S</font> st <br/>(  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Olive">F</font></span>)</span> &amp; ( for <font color="Olive">n</font> being  <a href="nat_1.html#NM1">Nat</a><br/> for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font>  st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Olive">F</font> &amp; <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Olive">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> holds <br/><font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Olive">y</font> ) )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:78"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">S</font>
 <b>by </b><i><a class="ref" href="mesfunc2.html#T34">MESFUNC2:34</a></i>;<br/>


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