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<b>let </b><font color="Maroon" title="c1">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">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/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">j</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:75_1"/>
<font color="Maroon" title="c3">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setwop_2.html#K2" title="SETWOP_2:func.2">Seg</a> <font color="Maroon" title="c1">i</font>
 ;<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>set </b><font color="Maroon" title="c5">r'</font> = <span class="p1">(<span class="default"><a href="rvsum_1.html#K7" title="RVSUM_1:func.7">-</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>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="rvsum_1.html#K13" title="RVSUM_1:func.13">sqr</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K7" title="RVSUM_1:func.7">-</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">j</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rvsum_1.html#K7" title="RVSUM_1:func.7">-</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></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#T78" target="_self" title="RVSUM_1:th.78">Th78</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="binop_2.html#K7" title="BINOP_2:func.7">-</a> <span class="p2">(<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>)</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#T35" target="_self" title="RVSUM_1:th.35">Th35</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> 

<br/>.= 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K13" title="RVSUM_1:func.13">sqr</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>
<b>by </b><i><a class="ref" href="rvsum_1.html#T78" target="_self" title="RVSUM_1:th.78">Th78</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:75"/>
 <a href="rvsum_1.html#K13" title="RVSUM_1:func.13">sqr</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K7" title="RVSUM_1:func.7">-</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K13" title="RVSUM_1:func.13">sqr</a> <font color="Maroon" title="c2">R</font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T139" title="FINSEQ_2:th.139">FINSEQ_2:139</a></i>;<br/>


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