<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c2">R</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">i</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>



<a NAME="E1:88"/><i><font color="Green" title="E38">A1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E2:88"/><b>then </b><i><font color="Green" title="E39">A2</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a>  <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T37" title="FINSEQ_2:th.37">FINSEQ_2:37</a></i>;<br/>
<a NAME="E3:88"/><i><font color="Green" title="E40">A3</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font>
 
<b>by </b><i><a class="txt" href="rvsum_1.html#E1:88"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="finseq_2.html#T86" title="FINSEQ_2:th.86">FINSEQ_2:86</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="88_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E1:88_1"/><i><font color="Green" title="E41">A4</font></i>: 
<font color="Maroon" title="c3">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">i</font>
 ;<br/><a NAME="E2:88_1"/><b>then </b><i><font color="Green" title="E42">A5</font></i>: 
<font color="Maroon" title="c3">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a>  <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c2">R</font></span>)</span>
 <b>by </b><i><a class="txt" href="rvsum_1.html#E2:88"><i><font color="Green" title="E39">A2</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E3:88_1"/><i><font color="Green" title="E43">A6</font></i>: 
<font color="Maroon" title="c3">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c2">R</font></span>)</span>
 <b>by </b><i><a class="txt" href="rvsum_1.html#E3:88"><i><font color="Green" title="E40">A3</font></i></a>, <a class="txt" href="rvsum_1.html#E1:88_1"><i><font color="Green" title="E41">A4</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><b>set </b><font color="Maroon" title="c4">r</font> = <font color="Maroon" title="c2">R</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">j</font>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a>  <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">j</font> = 
<a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">R</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">j</font></span>)</span>
<b>by </b><i><a class="txt" href="rvsum_1.html#E2:88_1"><i><font color="Green" title="E42">A5</font></i></a>, <a class="ref" href="funct_1.html#T22" title="FUNCT_1:th.22">FUNCT_1:22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">R</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">j</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> 
<b>by </b><i><a class="ref" href="rvsum_1.html#D2" target="_self" title="RVSUM_1:def.2">Def2</a></i>
<br/>.= 
<a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">R</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">j</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">R</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">j</font></span>)</span>
<b>by </b><i><a class="ref" href="binop_2.html#D11" title="BINOP_2:def.11">BINOP_2:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c2">R</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">j</font>
<b>by </b><i><a class="txt" href="rvsum_1.html#E3:88_1"><i><font color="Green" title="E43">A6</font></i></a>, <a class="ref" href="funcop_1.html#T28" title="FUNCOP_1:th.28">FUNCOP_1:28</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:88"/>
 <a href="rvsum_1.html#K13" title="RVSUM_1:func.13">sqr</a> <font color="Maroon" title="c2">R</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="rvsum_1.html#K15" title="RVSUM_1:func.15">mlt</a> <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c2">R</font>
 <b>by </b><i><a class="txt" href="rvsum_1.html#E2:88"><i><font color="Green" title="E39">A2</font></i></a>, <a class="txt" href="rvsum_1.html#E3:88"><i><font color="Green" title="E40">A3</font></i></a>, <a class="ref" href="finseq_2.html#T10" title="FINSEQ_2:th.10">FINSEQ_2:10</a></i>;<br/>


</div>
