<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">y</font>, <font color="Maroon" title="c2">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K27" title="SIN_COS:func.27">exp_R</a> <span class="p3">(<span class="default"><a href="binop_2.html#K7" title="BINOP_2:func.7">-</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K27" title="SIN_COS:func.27">exp_R</a> <span class="p3">(<span class="default"><a href="binop_2.html#K7" title="BINOP_2:func.7">-</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 2</span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> (<a href="power.html#K8" title="POWER:func.8">number_e</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> 1</span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1</span>)</span></span>)</span>)</span>)</span> )</span><br/>



<a NAME="E1:93"/><span class="lab"><font color="Green" title="E47">A1</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos.html#T55" title="SIN_COS:th.55">SIN_COS:55</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">t</font> =  <a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:93"/><span class="lab"><font color="Green" title="E48">A2</font></span>: 
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K27" title="SIN_COS:func.27">exp_R</a> <span class="p3">(<span class="default"><a href="binop_2.html#K7" title="BINOP_2:func.7">-</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K27" title="SIN_COS:func.27">exp_R</a> <span class="p3">(<span class="default"><a href="binop_2.html#K7" title="BINOP_2:func.7">-</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:93"/><span class="lab"><font color="Green" title="E49">A3</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 2</span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> (<a href="power.html#K8" title="POWER:func.8">number_e</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> 1</span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1</span>)</span></span>)</span>)</span>)</span></span><br/>

<a NAME="E4:93"/>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default">1 <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K27" title="SIN_COS:func.27">exp_R</a> <span class="p3">(<span class="default"><a href="binop_2.html#K7" title="BINOP_2:func.7">-</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:93"><span class="lab"><font color="Green" title="E48">A2</font></span></a>, <a class="ref" href="taylor_1.html#T4" title="TAYLOR_1:th.4">TAYLOR_1:4</a></span>;<br/>
<a NAME="E5:93"/><span class="kw">then </span>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default">1 <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p2">(<span class="default">1 <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="taylor_1.html#T4" title="TAYLOR_1:th.4">TAYLOR_1:4</a></span>;<br/>
<a NAME="E6:93"/><span class="kw">then </span>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default">1 <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1</span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:93"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="ref" href="xcmplx_1.html#T127" title="XCMPLX_1:th.127">XCMPLX_1:127</a></span>;<br/>
<a NAME="E7:93"/><span class="kw">then </span>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1</span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:93"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="ref" href="xcmplx_1.html#T113" title="XCMPLX_1:th.113">XCMPLX_1:113</a></span>;<br/>
<a NAME="E8:93"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A4</font></span>: 
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a></span>)</span></span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:93"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="ref" href="xcmplx_1.html#T55" title="XCMPLX_1:th.55">XCMPLX_1:55</a></span>;<br/>
<a NAME="E9:93"/><span class="kw">then </span>
<font color="Maroon" title="c1">y</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:93"><span class="lab"><font color="Green" title="E49">A3</font></span></a>, <a class="ref" href="sin_cos7.html#T30" target="_self" title="SIN_COS7:th.30">Th30</a>, <a class="ref" href="xcmplx_1.html#T87" title="XCMPLX_1:th.87">XCMPLX_1:87</a></span>;<br/>
<a NAME="E10:93"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A5</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> 1</span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1</span>)</span>
 
;<br/>
<a NAME="E11:93"/>
 <a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:93"><span class="lab"><font color="Green" title="E49">A3</font></span></a>, <a class="ref" href="sin_cos7.html#T29" target="_self" title="SIN_COS7:th.29">Th29</a></span>;<br/>
<a NAME="E12:93"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A6</font></span>: 
( 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">y</font> or <font color="Maroon" title="c1">y</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="binop_2.html#K19" title="BINOP_2:func.19">-</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:93"><span class="lab"><font color="Green" title="E50">A4</font></span></a>, <a class="txt" href="sin_cos7.html#E44"><span class="lab"><font color="Green" title="E36">Lm12</font></span></a>, <a class="ref" href="sin_cos.html#T55" title="SIN_COS:th.55">SIN_COS:55</a></span>;<br/>
<a NAME="E13:93"/><span class="kw">then </span>
( 1 <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">y</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1 or <font color="Maroon" title="c1">y</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="binop_2.html#K19" title="BINOP_2:func.19">-</a> 1</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T14" title="XREAL_1:th.14">XREAL_1:14</a></span>;<br/>
<a NAME="E14:93"/><span class="kw">then </span>
 <a href="square_1.html#K6" title="SQUARE_1:func.6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> 1</span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:93"><span class="lab"><font color="Green" title="E51">A5</font></span></a>, <a class="ref" href="xcmplx_1.html#T89" title="XCMPLX_1:th.89">XCMPLX_1:89</a></span>;<br/>
<a NAME="E15:93"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A7</font></span>: 
 <a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> 1</span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:93"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="ref" href="square_1.html#T22" title="SQUARE_1:th.22">SQUARE_1:22</a></span>;<br/>
<a NAME="E16:93"/><span class="lab"><font color="Green" title="E54">A8</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> 1</span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:93"><span class="lab"><font color="Green" title="E52">A6</font></span></a>, <a class="txt" href="sin_cos7.html#E39"><span class="lab"><font color="Green" title="E31">Lm7</font></span></a></span>;<br/>
<a NAME="E17:93"/><span class="kw">then </span>
 <a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> 1</span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> 1</span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1</span>)</span></span>)</span> <a href="power.html#K3" title="POWER:func.3">to_power</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="asympt_1.html#T83" title="ASYMPT_1:th.83">ASYMPT_1:83</a></span>;<br/>
<a NAME="E18:93"/><span class="kw">then </span>
 <a href="power.html#K5" title="POWER:func.5">log</a> (<a href="power.html#K8" title="POWER:func.8">number_e</a>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> 1</span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1</span>)</span></span>)</span> <a href="power.html#K3" title="POWER:func.3">to_power</a> <span class="p2">(<span class="default">1 <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 2</span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:93"><span class="lab"><font color="Green" title="E53">A7</font></span></a>, <a class="ref" href="taylor_1.html#T12" title="TAYLOR_1:th.12">TAYLOR_1:12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E19:93"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 2</span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> (<a href="power.html#K8" title="POWER:func.8">number_e</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> 1</span>)</span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">y</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:93"><span class="lab"><font color="Green" title="E54">A8</font></span></a>, <a class="txt" href="sin_cos7.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a>, <a class="ref" href="power.html#T55" title="POWER:th.55">POWER:55</a>, <a class="ref" href="taylor_1.html#T11" title="TAYLOR_1:th.11">TAYLOR_1:11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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