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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K1">REAL</a> ;<br/>





<a NAME="E1:62"/><i><font color="Green">E37</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K1">REAL</a> 
 
;<br/>
<a NAME="E2:62"/><i><font color="Green">E38</font></i>: 
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K1" target="_self">sqrreal</a>  <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K1">REAL</a> 
 
;<br/>
<b>thus </b> <a href="rvsum_1.html#K12" target="_self">sqr</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rvsum_1.html#K10" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<a href="rvsum_1.html#K1" target="_self">sqrreal</a>  <a href="finseqop.html#K5">*</a> <span class="p1">(<span class="default"><a href="binop_2.html#K35">multreal</a>  <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T44">FUNCOP_1:44</a></i>
<br/>.= 
<a href="rvsum_1.html#K1" target="_self">sqrreal</a>  <a href="finseqop.html#K5">*</a> <span class="p1">(<span class="default"><a href="binop_2.html#K35">multreal</a>  <a href="finseqop.html#K3">[;]</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="rvsum_1.html#E1:62"><i><font color="Green">E37</font></i></a>, <a class="ref" href="relat_1.html#T79">RELAT_1:79</a></i>
<br/>.= 
<a href="binop_2.html#K35">multreal</a>  <a href="finseqop.html#K3">[;]</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K1" target="_self">sqrreal</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="rvsum_1.html#K1" target="_self">sqrreal</a>  <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T17" target="_self">Th17</a>, <a class="ref" href="finseqop.html#T53">FINSEQOP:53</a></i>
<br/>.= 
<a href="binop_2.html#K35">multreal</a>  <a href="finseqop.html#K3">[;]</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K1" target="_self">sqrreal</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span> <a href="finseqop.html#K5">*</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K1" target="_self">sqrreal</a>  <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="rvsum_1.html#E2:62"><i><font color="Green">E38</font></i></a>, <a class="ref" href="relat_1.html#T79">RELAT_1:79</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="binop_2.html#K35">multreal</a>  <a href="funcop_1.html#K8">[;]</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K1" target="_self">sqrreal</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="finseqop.html#K5">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K1" target="_self">sqrreal</a>  <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T44">FUNCOP_1:44</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="rvsum_1.html#K10" target="_self">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K12" target="_self">sqr</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#D2" target="_self">Def2</a></i>
;<br/>


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