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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_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/>





<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#K8" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
 <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#K4" target="_self">+</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K6" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T52" target="_self">Th52</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rvsum_1.html#K12" target="_self">sqr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rvsum_1.html#K4" target="_self">+</a> <span class="p2">(<span class="default">2 <a href="rvsum_1.html#K10" target="_self">*</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K14" target="_self">mlt</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="rvsum_1.html#K6" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rvsum_1.html#K4" target="_self">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K12" target="_self">sqr</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K6" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T98" target="_self">Th98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rvsum_1.html#K12" target="_self">sqr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rvsum_1.html#K4" target="_self">+</a> <span class="p2">(<span class="default">2 <a href="rvsum_1.html#K10" target="_self">*</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K14" target="_self">mlt</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="rvsum_1.html#K6" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rvsum_1.html#K4" 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#T83" target="_self">Th83</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rvsum_1.html#K12" target="_self">sqr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rvsum_1.html#K4" target="_self">+</a> <span class="p2">(<span class="default">2 <a href="rvsum_1.html#K10" target="_self">*</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K14" target="_self">mlt</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="binop_2.html#K7">-</a> 1</span>)</span> <a href="rvsum_1.html#K10" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rvsum_1.html#K4" 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#T76" target="_self">Th76</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rvsum_1.html#K12" target="_self">sqr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rvsum_1.html#K4" target="_self">+</a> <span class="p2">(<span class="default">2 <a href="rvsum_1.html#K10" target="_self">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binop_2.html#K7">-</a> 1</span>)</span> <a href="rvsum_1.html#K10" target="_self">*</a> <span class="p4">(<span class="default"><a href="rvsum_1.html#K14" target="_self">mlt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rvsum_1.html#K4" 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#T94" target="_self">Th94</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rvsum_1.html#K12" target="_self">sqr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rvsum_1.html#K4" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="binop_2.html#K7">-</a> 1</span>)</span> <a href="binop_2.html#K11">*</a> 2</span>)</span> <a href="rvsum_1.html#K10" target="_self">*</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K14" target="_self">mlt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="rvsum_1.html#K4" 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#T71" target="_self">Th71</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rvsum_1.html#K12" target="_self">sqr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rvsum_1.html#K4" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binop_2.html#K7">-</a> 1</span>)</span> <a href="rvsum_1.html#K10" target="_self">*</a> <span class="p3">(<span class="default">2 <a href="rvsum_1.html#K10" target="_self">*</a> <span class="p4">(<span class="default"><a href="rvsum_1.html#K14" target="_self">mlt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rvsum_1.html#K4" 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#T71" target="_self">Th71</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rvsum_1.html#K12" target="_self">sqr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rvsum_1.html#K4" target="_self">+</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K6" target="_self">-</a> <span class="p3">(<span class="default">2 <a href="rvsum_1.html#K10" target="_self">*</a> <span class="p4">(<span class="default"><a href="rvsum_1.html#K14" target="_self">mlt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rvsum_1.html#K4" 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#T76" target="_self">Th76</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rvsum_1.html#K12" target="_self">sqr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rvsum_1.html#K8" target="_self">-</a> <span class="p2">(<span class="default">2 <a href="rvsum_1.html#K10" target="_self">*</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K14" target="_self">mlt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="rvsum_1.html#K4" 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#T52" target="_self">Th52</a></i>
;<br/>


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