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<b>let </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>





<a NAME="E1:6"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>9</sub></font> is   <a href="real_1.html#NM1">Real</a>
 
<b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<b>thus </b> <a href="sin_cos.html#K23">cos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> = 
<a href="sin_cos.html#K22">cos</a>  <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos.html#D23">SIN_COS:def 23</a></i>
<br/>.= 
<a href="sin_cos.html#K22">cos</a>  <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan16.html#K1">AffineMap</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="jordan16.html#D3">JORDAN16:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="sin_cos.html#K22">cos</a>  <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="jordan16.html#K1">AffineMap</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="toprealb.html#E1:6"><i><font color="Green">E13</font></i></a>, <a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
;<br/>


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