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<span class="kw">let </span><font color="Maroon" title="c1">r1</font>, <font color="Maroon" title="c2">r2</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> (<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">r1</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>,<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c2">r2</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <font color="Maroon" title="c2">r2</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c3">s1</font> = <font color="Maroon" title="c1">r1</font>, <font color="Maroon" title="c4">s2</font> = <font color="Maroon" title="c2">r2</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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></span>;<br/>
 <a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> (<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">s1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>,<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">s2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>) = 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font>)</span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T74" title="FINSEQ_2:th.74">FINSEQ_2:74</a></span>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <font color="Maroon" title="c2">r2</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binop_2.html#D11" title="BINOP_2:def.11">BINOP_2:def 11</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:63"/>
 <a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> (<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c1">r1</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>,<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c2">r2</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <font color="Maroon" title="c2">r2</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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