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<b>let </b><font color="Maroon">x</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:18"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 ;<br/>

<a NAME="E2:18"/><b>then </b>
(  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">x</font> &amp; <font color="Maroon">x</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2 )
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T47">RCOMP_1:47</a></i>;<br/>
<a NAME="E3:18"/><b>then </b>
( <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2</span>)</span> &amp; <font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2</span>)</span> )
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E4:18"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default">0,<a href="sin_cos.html#K35">PI</a> </span><a href="rcomp_1.html#K2">.[</a></span>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T47">RCOMP_1:47</a></i>;<br/>
<a NAME="E5:18"/>
<a href="sin_cos.html#K19">sin</a>  <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K35">PI</a>  <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <a href="sin_cos.html#K22">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="sin_cos.html#T83">SIN_COS:83</a></i>;<br/>
<b>hence </b><a NAME="E6:18"/>
<a href="sin_cos.html#K22">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i>, </i>;<br/>


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