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<span class="lab"><font color="Green" title="E52">A1</font></span>: <a href="fdiff_9.html#K1" title="FDIFF_9:func.1">sec</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  = 
1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="sincos10.html#E18"><span class="lab"><font color="Green" title="E14">Lm6</font></span></a>, <a class="ref" href="sincos10.html#T2" target="_self" title="SINCOS10:th.2">Th2</a>, <a class="ref" href="rfunct_1.html#D8" title="RFUNCT_1:def.8">RFUNCT_1:def 8</a>, <a class="ref" href="sin_cos.html#T81" title="SIN_COS:th.81">SIN_COS:81</a></span>
<br/>.= 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1

;<br/>
<span class="lab"><font color="Green" title="E53">A2</font></span>: <a href="fdiff_9.html#K1" title="FDIFF_9:func.1">sec</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a> </span>)</span> = 
1 <a href="real_1.html#K10" title="REAL_1:func.10">/</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</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="sincos10.html#E18"><span class="lab"><font color="Green" title="E14">Lm6</font></span></a>, <a class="ref" href="sincos10.html#T2" target="_self" title="SINCOS10:th.2">Th2</a>, <a class="ref" href="sincos10.html#T30" target="_self" title="SINCOS10:th.30">Th30</a>, <a class="ref" href="rfunct_1.html#D8" title="RFUNCT_1:def.8">RFUNCT_1:def 8</a></span>
<br/>.= 
 <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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</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="ref" href="xcmplx_1.html#T189" title="XCMPLX_1:th.189">XCMPLX_1:189</a></span>
<br/>.= 
 <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> 2</span>)</span>

;<br/>
<span class="lab"><font color="Green" title="E54">A3</font></span>: <a href="fdiff_9.html#K1" title="FDIFF_9:func.1">sec</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  = 
1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="sincos10.html#E17"><span class="lab"><font color="Green" title="E13">Lm5</font></span></a>, <a class="ref" href="sincos10.html#T1" target="_self" title="SINCOS10:th.1">Th1</a>, <a class="ref" href="rfunct_1.html#D8" title="RFUNCT_1:def.8">RFUNCT_1:def 8</a>, <a class="ref" href="sin_cos.html#T33" title="SIN_COS:th.33">SIN_COS:33</a></span>
<br/>.= 
1

;<br/>
<a href="fdiff_9.html#K1" title="FDIFF_9:func.1">sec</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span> = 
1 <a href="real_1.html#K10" title="REAL_1:func.10">/</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="sincos10.html#E17"><span class="lab"><font color="Green" title="E13">Lm5</font></span></a>, <a class="ref" href="sincos10.html#T1" target="_self" title="SINCOS10:th.1">Th1</a>, <a class="ref" href="sincos10.html#T29" target="_self" title="SINCOS10:th.29">Th29</a>, <a class="ref" href="rfunct_1.html#D8" title="RFUNCT_1:def.8">RFUNCT_1:def 8</a></span>
<br/>.= 
 <a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> 2

;<br/>
<span class="kw">hence </span><a NAME="E5:37"/>
( <a href="fdiff_9.html#K1" title="FDIFF_9:func.1">sec</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <a href="fdiff_9.html#K1" title="FDIFF_9:func.1">sec</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</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> 2 &amp; <a href="fdiff_9.html#K1" title="FDIFF_9:func.1">sec</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 4</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a> </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> 2</span>)</span> &amp; <a href="fdiff_9.html#K1" title="FDIFF_9:func.1">sec</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <a href="sin_cos.html#K36" title="SIN_COS:func.36">PI</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="#E3:37"><span class="lab"><font color="Green" title="E54">A3</font></span></a>, <a class="txt" href="#E2:37"><span class="lab"><font color="Green" title="E53">A2</font></span></a>, <a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E52">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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