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<b>let </b><font color="Maroon" title="c1">r</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>let </b><font color="Maroon" title="c2">F</font> be  <a href="seq_1.html#NV1" title="SEQ_1:NV.1">real-yielding</a> <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>;<br/>



<b>reconsider </b><font color="Maroon" title="c3">s</font> = <font color="Maroon" title="c1">r</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <b>by </b><i><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></i>;<br/>
<b>set </b><font color="Maroon" title="c4">rM</font> = <a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="funcop_1.html#K10" title="FUNCOP_1:func.10">[;]</a> <font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> </span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">F1</font> = <font color="Maroon" title="c2">F</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <b>by </b><i><a class="txt" href="rvsum_1.html#E31"><i><font color="Green" title="E10">Lm4</font></i></a></i>;<br/>
<b>thus </b> <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c2">F</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="funcop_1.html#K10" title="FUNCOP_1:func.10">[;]</a> <font color="Maroon" title="c3">s</font>,<span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> </span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><a href="binop_2.html#K33" title="BINOP_2:func.33">addreal</a>  <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <font color="Maroon" title="c5">F1</font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T16" target="_self" title="RVSUM_1:th.16">Th16</a>, <a class="ref" href="rvsum_1.html#T22" target="_self" title="RVSUM_1:th.22">Th22</a>, <a class="ref" href="setwop_2.html#T41" title="SETWOP_2:th.41">SETWOP_2:41</a></i>
<br/>.= 
<font color="Maroon" title="c1">r</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <font color="Maroon" title="c5">F1</font></span>)</span>
<b>by </b><i><a class="txt" href="rvsum_1.html#E23"><i><font color="Green" title="E6">Lm3</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c1">r</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K16" title="RVSUM_1:func.16">Sum</a> <font color="Maroon" title="c2">F</font></span>)</span>

;<br/>


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