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<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">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="c3">x</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>





<b>assume </b><a NAME="E1:16"/>
2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">m</font>
 ;<br/>

<a NAME="E2:16"/><b>then </b><i><font color="Green" title="E15">A1</font></i>: 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 2 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 
<b>by </b><i><a class="txt" href="jordan1d.html#E13"><i><font color="Green" title="E9">Lm5</font></i></a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">2 <a href="newton.html#K3" title="NEWTON:func.3">|^</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 2</span>)</span> = 
<font color="Maroon" title="c3">x</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K3" title="NEWTON:func.3">|^</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T82" title="XCMPLX_1:th.82">XCMPLX_1:82</a></i>
<br/>.= 
<font color="Maroon" title="c3">x</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K3" title="NEWTON:func.3">|^</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 2</span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 2</span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T92" title="XCMPLX_1:th.92">XCMPLX_1:92</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K3" title="NEWTON:func.3">|^</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 2</span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T82" title="XCMPLX_1:th.82">XCMPLX_1:82</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">2 <a href="newton.html#K3" title="NEWTON:func.3">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 2</span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11" title="NEWTON:th.11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">2 <a href="newton.html#K3" title="NEWTON:func.3">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 2</span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="jordan1d.html#E2:16"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="binarith.html#D3" title="BINARITH:def.3">BINARITH:def 3</a></i>
;<br/>


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