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<b>let </b><font color="Maroon" title="c1">r</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><b>let </b><font color="Maroon" title="c2">j</font>, <font color="Maroon" title="c3">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>assume </b><a NAME="E1:9"/><i><font color="Green" title="E8">A1</font></i>: 
( <font color="Maroon" title="c1">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">i</font> )
 ;<br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="newton.html#K3" title="NEWTON:func.3">|^</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="newton.html#K3" title="NEWTON:func.3">|^</a> <font color="Maroon" title="c2">j</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K21" title="RVSUM_1:func.21">Product</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="newton.html#K1" title="NEWTON:func.1">|-&gt;</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="newton.html#K3" title="NEWTON:func.3">|^</a> <font color="Maroon" title="c2">j</font></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#D1" title="NEWTON:def.1">NEWTON:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K21" title="RVSUM_1:func.21">Product</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="newton.html#K1" title="NEWTON:func.1">|-&gt;</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K21" title="RVSUM_1:func.21">Product</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="newton.html#K1" title="NEWTON:func.1">|-&gt;</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#D1" title="NEWTON:def.1">NEWTON:def 1</a></i>
<br/>.= 
 <a href="rvsum_1.html#K21" title="RVSUM_1:func.21">Product</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c2">j</font></span>)</span> <a href="newton.html#K1" title="NEWTON:func.1">|-&gt;</a> <font color="Maroon" title="c1">r</font></span>)</span>
<b>by </b><i><a class="txt" href="topreal6.html#E1:9"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="topreal6.html#T14" target="_self" title="TOPREAL6:th.14">Th14</a></i>
<br/>.= 
<font color="Maroon" title="c1">r</font> <a href="newton.html#K3" title="NEWTON:func.3">|^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c2">j</font></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#D1" title="NEWTON:def.1">NEWTON:def 1</a></i>
;<br/>


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