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<a NAME="E1:123_1_1"/><span class="lab"><font color="Green" title="E97">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="sin_cos.html#K33" title="SIN_COS:func.33">tan</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">tan</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">r</font> where <font color="Olive" title="b1">r</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : ( <a href="sin_cos.html#K33" title="SIN_COS:func.33">tan</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="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">r</font> &amp; <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="sin_cos.html#K33" title="SIN_COS:func.33">tan</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1 ) </span>}</span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rcomp_1.html#D1" title="RCOMP_1:def.1">RCOMP_1:def 1</a></span>;<br/>
<a NAME="E2:123_1_1"/><span class="lab"><font color="Green" title="E98">A2</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="sin_cos.html#K33" title="SIN_COS:func.33">tan</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">tan</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="sin_cos.html#E127"><span class="lab"><font color="Green" title="E96">Lm17</font></span></a>, <a class="ref" href="xxreal_1.html#T29" title="XXREAL_1:th.29">XXREAL_1:29</a></span>;<br/>
<a NAME="E3:123_1_1"/><span class="lab"><font color="Green" title="E99">A3</font></span>: 
1 <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="sin_cos.html#K33" title="SIN_COS:func.33">tan</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">tan</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</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="sin_cos.html#K33" title="SIN_COS:func.33">tan</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K33" title="SIN_COS:func.33">tan</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </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="#E1:123_1_1"><span class="lab"><font color="Green" title="E97">A1</font></span></a>, <a class="txt" href="#E2:123_1_1"><span class="lab"><font color="Green" title="E98">A2</font></span></a>, <a class="txt" href="sin_cos.html#E127"><span class="lab"><font color="Green" title="E96">Lm17</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c3">th</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E5:123_1_1"/><span class="lab"><font color="Green" title="E100">A4</font></span>: 
<font color="Maroon" title="c3">th</font> <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"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 <span class="kw">and </span><br/><a NAME="E6:123_1_1"/><span class="lab"><font color="Green" title="E101">A5</font></span>: 
<a href="sin_cos.html#K33" title="SIN_COS:func.33">tan</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">th</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:123_1_1"><span class="lab"><font color="Green" title="E99">A3</font></span></a>, <a class="ref" href="sin_cos.html#T75" target="_self" title="SIN_COS:th.75">Th75</a>, <a class="ref" href="sin_cos.html#T76" target="_self" title="SIN_COS:th.76">Th76</a>, <a class="ref" href="fcont_2.html#T16" title="FCONT_2:th.16">FCONT_2:16</a></span>;<br/>
<a NAME="E7:123_1_1"/><span class="lab"><font color="Green" title="E102">A6</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">th</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:123_1_1"><span class="lab"><font color="Green" title="E100">A4</font></span></a>, <a class="ref" href="xxreal_1.html#T1" title="XXREAL_1:th.1">XXREAL_1:1</a></span>;<br/>
<a NAME="E8:123_1_1"/><span class="lab"><font color="Green" title="E103">A7</font></span>: 
<font color="Maroon" title="c3">th</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:123_1_1"><span class="lab"><font color="Green" title="E100">A4</font></span></a>, <a class="ref" href="xxreal_1.html#T1" title="XXREAL_1:th.1">XXREAL_1:1</a></span>;<br/>
<a NAME="E9:123_1_1"/><span class="lab"><font color="Green" title="E104">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> <font color="Maroon" title="c3">th</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:123_1_1"><span class="lab"><font color="Green" title="E101">A5</font></span></a>, <a class="txt" href="#E7:123_1_1"><span class="lab"><font color="Green" title="E102">A6</font></span></a>, <a class="txt" href="sin_cos.html#E127"><span class="lab"><font color="Green" title="E96">Lm17</font></span></a></span>;<br/>
<a NAME="E10:123_1_1"/><span class="lab"><font color="Green" title="E105">A9</font></span>: 
<font color="Maroon" title="c3">th</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:123_1_1"><span class="lab"><font color="Green" title="E101">A5</font></span></a>, <a class="txt" href="#E8:123_1_1"><span class="lab"><font color="Green" title="E103">A7</font></span></a>, <a class="txt" href="sin_cos.html#E127"><span class="lab"><font color="Green" title="E96">Lm17</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/>
<span class="kw">take </span><font color="Maroon" title="c4">th1</font> = <font color="Maroon" title="c3">th</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 4; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <a href="sin_cos.html#K33" title="SIN_COS:func.33">tan</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">th1</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c4">th1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,4</span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span> )</span><br/>

<span class="kw">thus </span><a NAME="E11:123_1_1"/>
<a href="sin_cos.html#K33" title="SIN_COS:func.33">tan</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">th1</font> <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> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:123_1_1"><span class="lab"><font color="Green" title="E101">A5</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"> <font color="Maroon" title="c4">th1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,4</span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span></span><br/>

<a NAME="E12:123_1_1"/><span class="lab"><font color="Green" title="E106">A10</font></span>: 
<font color="Maroon" title="c3">th</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 4 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 4
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:123_1_1"><span class="lab"><font color="Green" title="E105">A9</font></span></a>, <a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></span>;<br/>
<span class="kw">thus </span><a NAME="E13:123_1_1"/>
<font color="Maroon" title="c4">th1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,4</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="#E9:123_1_1"><span class="lab"><font color="Green" title="E104">A8</font></span></a>, <a class="txt" href="#E12:123_1_1"><span class="lab"><font color="Green" title="E106">A10</font></span></a>, <a class="ref" href="xxreal_1.html#T4" title="XXREAL_1:th.4">XXREAL_1:4</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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