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<span class="lab"><font color="Green" title="E11">A1</font></span>:  <a href="sin_cos.html#K22" title="SIN_COS:func.22">cos</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> 2</span>)</span></span>)</span> = 
 <a href="sin_cos.html#K19" title="SIN_COS:func.19">sin</a> <span class="p1">(<span class="default"><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> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <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>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos.html#T79" title="SIN_COS:th.79">SIN_COS:79</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos.html#T77" title="SIN_COS:th.77">SIN_COS:77</a></span>
;<br/>
<a NAME="E2:10"/><span class="lab"><font color="Green" title="E12">A2</font></span>: 
 <a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> 2 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="square_1.html#T25" title="SQUARE_1:th.25">SQUARE_1:25</a></span>;<br/>
<a NAME="E3:10"/>
 <a href="sin_cos.html#K19" title="SIN_COS:func.19">sin</a> <span class="p1">(<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> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <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="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K22" title="SIN_COS:func.22">cos</a> <span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p0">(<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>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="integra8.html#E2"><span class="lab"><font color="Green" title="E2">Lm2</font></span></a>, <a class="ref" href="integra8.html#T6" target="_self" title="INTEGRA8:th.6">Th6</a></span>;<br/>
<span class="kw">then </span> <a href="sin_cos.html#K19" title="SIN_COS:func.19">sin</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> = 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="square_1.html#T18" title="SQUARE_1:th.18">SQUARE_1:18</a>, <a class="ref" href="square_1.html#T30" title="SQUARE_1:th.30">SQUARE_1:30</a></span>
<br/>.= 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> 2</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="xcmplx_1.html#T91" title="XCMPLX_1:th.91">XCMPLX_1:91</a></span>
<br/>.= 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> 2</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> 2</span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span></span>)</span>

;<br/>
<span class="kw">hence </span><a NAME="E5:10"/>
 <a href="sin_cos.html#K19" title="SIN_COS:func.19">sin</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> <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"><span class="p2">(<span class="default"><a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> 2</span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="square_1.html#D2" title="SQUARE_1:def.2">SQUARE_1:def 2</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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