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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>, <font color="Maroon">c<sub>3</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:11"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K8">-</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<i><font color="Green">E12</font></i>: <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid.html#K12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="euclid.html#K12">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3"><a href="euclid.html#K12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K8">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="euclid.html#K12">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p4">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p5">(<span class="default"><a href="euclid.html#K11">sqr</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3"><a href="euclid.html#K12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K8">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="euclid.html#K12">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#D5">EUCLID:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p4">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p5">(<span class="default"><a href="euclid.html#K11">sqr</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p4">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p5">(<span class="default"><a href="euclid.html#K11">sqr</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K8">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#D5">EUCLID:def 5</a></i>
;<br/>
<a NAME="E3:11"/>
 <a href="rvsum_1.html#K15">Sum</a> <span class="p1">(<span class="default"><a href="euclid.html#K11">sqr</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="rvsum_1.html#T116">RVSUM_1:116</a></i>;<br/>
<a NAME="E4:11"/><b>then </b><i><font color="Green">E13</font></i>: 
<span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p3">(<span class="default"><a href="euclid.html#K11">sqr</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a>  <a href="hidden.html#R1">=</a>  <a href="rvsum_1.html#K15">Sum</a> <span class="p1">(<span class="default"><a href="euclid.html#K11">sqr</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>;<br/>
<a NAME="E5:11"/>
 <a href="rvsum_1.html#K15">Sum</a> <span class="p1">(<span class="default"><a href="euclid.html#K11">sqr</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K8">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="rvsum_1.html#T116">RVSUM_1:116</a></i>;<br/>
<a NAME="E6:11"/><b>then </b><i><font color="Green">E14</font></i>: 
<span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p3">(<span class="default"><a href="euclid.html#K11">sqr</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K8">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5">^2</a>  <a href="hidden.html#R1">=</a>  <a href="rvsum_1.html#K15">Sum</a> <span class="p1">(<span class="default"><a href="euclid.html#K11">sqr</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K8">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="square_1.html#D4">SQUARE_1:def 4</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="euclid.html#K11">sqr</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="euclid.html#K11">sqr</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K8">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <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>  <b>by </b><i><a class="ref" href="euclid.html#D1">EUCLID:def 1</a></i>;<br/>
<a NAME="E8:11"/><i><font color="Green">E15</font></i>: 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2">(<span class="default"><a href="euclid.html#K11">sqr</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2">(<span class="default"><a href="euclid.html#K11">sqr</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K8">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rvsum_1.html#K15">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K11">sqr</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K8">-</a> <span class="p2">(<span class="default"><a href="euclid.html#K11">sqr</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K8">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="rvsum_1.html#T120">RVSUM_1:120</a></i>;<br/>
<span class="p1">(<span class="default"><a href="euclid.html#K11">sqr</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K8">-</a> <span class="p1">(<span class="default"><a href="euclid.html#K11">sqr</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K8">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p3">(<span class="default">2 <a href="rvsum_1.html#K10">*</a> <span class="p4">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K8">-</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rvsum_1.html#K8">-</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T98">RVSUM_1:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p3">(<span class="default">2 <a href="rvsum_1.html#K10">*</a> <span class="p4">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="rvsum_1.html#K8">-</a> <span class="p3">(<span class="default">2 <a href="rvsum_1.html#K10">*</a> <span class="p4">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T99">RVSUM_1:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="rvsum_1.html#K10">*</a> <span class="p4">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="rvsum_1.html#K8">-</a> <span class="p3">(<span class="default">2 <a href="rvsum_1.html#K10">*</a> <span class="p4">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T32">RVSUM_1:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="rvsum_1.html#K10">*</a> <span class="p5">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p4">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="rvsum_1.html#K8">-</a> <span class="p3">(<span class="default">2 <a href="rvsum_1.html#K10">*</a> <span class="p4">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rvsum_1.html#K8">-</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T60">RVSUM_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="rvsum_1.html#K10">*</a> <span class="p0">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p5">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p4">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K8">-</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p2">(<span class="default">2 <a href="rvsum_1.html#K10">*</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="rvsum_1.html#K8">-</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T62">RVSUM_1:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="rvsum_1.html#K10">*</a> <span class="p4">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p2">(<span class="default">2 <a href="rvsum_1.html#K10">*</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="rvsum_1.html#K8">-</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T63">RVSUM_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="rvsum_1.html#K10">*</a> <span class="p4">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p3">(<span class="default">2 <a href="rvsum_1.html#K10">*</a> <span class="p4">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K8">-</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K12">sqr</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T32">RVSUM_1:32</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="rvsum_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="rvsum_1.html#K4">+</a> <span class="p1">(<span class="default">2 <a href="rvsum_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T63">RVSUM_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K2">+</a> 2</span>)</span> <a href="rvsum_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T72">RVSUM_1:72</a></i>
<br/>.= 
4 <a href="rvsum_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span>

;<br/>
<b>then </b><span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid.html#K12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="euclid.html#K12">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3"><a href="euclid.html#K12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K8">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="euclid.html#K12">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="euclid_2.html#E2:11"><i><font color="Green">E12</font></i></a>, <a class="txt" href="euclid_2.html#E4:11"><i><font color="Green">E13</font></i></a>, <a class="txt" href="euclid_2.html#E6:11"><i><font color="Green">E14</font></i></a>, <a class="txt" href="euclid_2.html#E8:11"><i><font color="Green">E15</font></i></a>, <a class="ref" href="rvsum_1.html#T117">RVSUM_1:117</a></i>
<br/>.= 
 <a href="rvsum_1.html#K15">Sum</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span>)</span>

;<br/>
<b>hence </b><a NAME="E11:11"/>
<span class="p1"><a href="euclid_2.html#K1" target="_self">|(</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="euclid_2.html#K1" target="_self">)|</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="euclid.html#K12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K7">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="euclid.html#K12">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3"><a href="euclid.html#K12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="euclid.html#K8">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="euclid.html#K12">.|</a></span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="euclid_2.html#E1:11"><i><font color="Green">E11</font></i></a></i>;<br/>


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