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<b>let </b><font color="Maroon">C</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">c</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">r</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">C</font>, <a href="numbers.html#K1">REAL</a> ;<br/>







<b>assume </b><a NAME="E1:65"/>
<font color="Maroon">f</font> is <a href="partfun1.html#V1">total</a>
 ;<br/>

<a NAME="E2:65"/><b>then </b>
<font color="Maroon">r</font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f</font> is <a href="partfun1.html#V1">total</a>
 
<b>by </b><i/>;<br/>
<a NAME="E3:65"/><b>then </b>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="partfun1.html#D4">PARTFUN1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E4:65"/>
<span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">f</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c</font></span>)</span>
 <b>by </b><i><a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>;<br/>


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