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<span class="kw">let </span><font color="Maroon" title="c1">r</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">r</font> &amp; <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 implies  <a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span> )</span><br/>

<a NAME="E1:68"/><span class="lab"><font color="Green" title="E59">A1</font></span>: 
<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="sin_cos9.html#E23"><span class="lab"><font color="Green" title="E13">Lm7</font></span></a>, <a class="txt" href="sin_cos9.html#E24"><span class="lab"><font color="Green" title="E14">Lm8</font></span></a>, <a class="ref" href="xxreal_2.html#D12" title="XXREAL_2:def.12">XXREAL_2:def 12</a></span>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:68"/><span class="lab"><font color="Green" title="E60">A2</font></span>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">r</font>
 <span class="kw">and </span><br/><a NAME="E3:68"/><span class="lab"><font color="Green" title="E61">A3</font></span>: 
<font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span></span><br/>

<a NAME="E4:68"/><span class="lab"><font color="Green" title="E62">A4</font></span>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:68"><span class="lab"><font color="Green" title="E61">A3</font></span></a>, <a class="ref" href="xreal_1.html#T24" title="XREAL_1:th.24">XREAL_1:24</a></span>;<br/>
<a NAME="E5:68"/><span class="lab"><font color="Green" title="E63">A5</font></span>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:68"><span class="lab"><font color="Green" title="E60">A2</font></span></a>, <a class="ref" href="xreal_1.html#T24" title="XREAL_1:th.24">XREAL_1:24</a></span>;<br/>
<a NAME="E6:68"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A6</font></span>: 
 <a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:68"><span class="lab"><font color="Green" title="E62">A4</font></span></a>, <a class="ref" href="sin_cos9.html#T63" target="_self" title="SIN_COS9:th.63">Th63</a></span>;<br/>
<a NAME="E7:68"/>
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:68"><span class="lab"><font color="Green" title="E63">A5</font></span></a>, <a class="txt" href="#E4:68"><span class="lab"><font color="Green" title="E62">A4</font></span></a>, <a class="ref" href="sin_cos9.html#T63" target="_self" title="SIN_COS9:th.63">Th63</a></span>;<br/>
<a NAME="E8:68"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A7</font></span>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T24" title="XREAL_1:th.24">XREAL_1:24</a></span>;<br/>
<a NAME="E9:68"/>
 <a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:68"><span class="lab"><font color="Green" title="E63">A5</font></span></a>, <a class="txt" href="#E4:68"><span class="lab"><font color="Green" title="E62">A4</font></span></a>, <a class="ref" href="sin_cos9.html#T63" target="_self" title="SIN_COS9:th.63">Th63</a></span>;<br/>
<a NAME="E10:68"/><span class="kw">then </span>
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T24" title="XREAL_1:th.24">XREAL_1:24</a></span>;<br/>
<a NAME="E11:68"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A8</font></span>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:68"><span class="lab"><font color="Green" title="E65">A7</font></span></a>, <a class="ref" href="xxreal_1.html#T1" title="XXREAL_1:th.1">XXREAL_1:1</a></span>;<br/>
<a NAME="E12:68"/>
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:68"><span class="lab"><font color="Green" title="E63">A5</font></span></a>, <a class="txt" href="#E4:68"><span class="lab"><font color="Green" title="E62">A4</font></span></a>, <a class="ref" href="sin_cos9.html#T63" target="_self" title="SIN_COS9:th.63">Th63</a></span>;<br/>
<a NAME="E13:68"/><span class="kw">then </span>
 <a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:68"><span class="lab"><font color="Green" title="E64">A6</font></span></a>, <a class="ref" href="xxreal_1.html#T1" title="XXREAL_1:th.1">XXREAL_1:1</a></span>;<br/>
<a NAME="E14:68"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A9</font></span>: 
 <a href="sin_cos.html#K22" title="SIN_COS:func.22">cos</a> <span class="p1">(<span class="default"><a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:68"><span class="lab"><font color="Green" title="E59">A1</font></span></a>, <a class="ref" href="comptrig.html#T11" title="COMPTRIG:th.11">COMPTRIG:11</a></span>;<br/>
<a NAME="E15:68"/>
 <a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <span class="p1">(<span class="default"><a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:68"><span class="lab"><font color="Green" title="E63">A5</font></span></a>, <a class="txt" href="#E4:68"><span class="lab"><font color="Green" title="E62">A4</font></span></a>, <a class="ref" href="sin_cos9.html#T51" target="_self" title="SIN_COS9:th.51">Th51</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E68">A10</font></span>: <font color="Maroon" title="c1">r</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <span class="p3">(<span class="default"><a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <span class="p4">(<span class="default"><a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos9.html#T41" target="_self" title="SIN_COS9:th.41">Th41</a></span>
<br/>.= 
 <a href="sin_cos4.html#K1" title="SIN_COS4:func.1">tan</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:68"><span class="lab"><font color="Green" title="E67">A9</font></span></a>, <a class="ref" href="sin_cos.html#T31" title="SIN_COS:th.31">SIN_COS:31</a>, <a class="ref" href="sin_cos4.html#T8" title="SIN_COS4:th.8">SIN_COS4:8</a></span>
;<br/>
<a NAME="E17:68"/><span class="lab"><font color="Green" title="E69">A11</font></span>: 
<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="sin_cos9.html#E23"><span class="lab"><font color="Green" title="E13">Lm7</font></span></a>, <a class="txt" href="sin_cos9.html#E24"><span class="lab"><font color="Green" title="E14">Lm8</font></span></a>, <a class="ref" href="xxreal_2.html#D12" title="XXREAL_2:def.12">XXREAL_2:def 12</a></span>;<br/>
<a NAME="E18:68"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A12</font></span>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:68"><span class="lab"><font color="Green" title="E66">A8</font></span></a>, <a class="ref" href="xxreal_1.html#T4" title="XXREAL_1:th.4">XXREAL_1:4</a></span>;<br/>
<a NAME="E19:68"/>
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:68"><span class="lab"><font color="Green" title="E66">A8</font></span></a>, <a class="txt" href="#E17:68"><span class="lab"><font color="Green" title="E69">A11</font></span></a>, <a class="ref" href="xxreal_1.html#T4" title="XXREAL_1:th.4">XXREAL_1:4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E20:68"/>
 <a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="sin_cos9.html#K5" title="SIN_COS9:func.5">arctan</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c1">r</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:68"><span class="lab"><font color="Green" title="E68">A10</font></span></a>, <a class="txt" href="#E18:68"><span class="lab"><font color="Green" title="E70">A12</font></span></a>, <a class="ref" href="sin_cos9.html#T35" target="_self" title="SIN_COS9:th.35">Th35</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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