<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>

<a NAME="E1:18"/><i><font color="Green">E13</font></i>: 
 <a href="sin_cos.html#K19">sin</a>  <a href="fdiff_1.html#R2">is_differentiable_on</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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span>
 
<b>by </b><i><a class="ref" href="fdiff_1.html#T34">FDIFF_1:34</a>, <a class="ref" href="sin_cos.html#T73">SIN_COS:73</a></i>;<br/>
<a NAME="E2:18"/><b>then </b><i><font color="Green">E14</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K19">sin</a>  <a href="fdiff_1.html#K2">`|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="hidden.html#R1">=</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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span>
 
<b>by </b><i><a class="ref" href="fdiff_1.html#D8">FDIFF_1:def 8</a></i>;<br/>
<a NAME="E3:18"/><i><font color="Green">E15</font></i>: 
 <a href="sin_cos.html#K22">cos</a>  <a href="fdiff_1.html#R2">is_differentiable_on</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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span>
 
<b>by </b><i><a class="ref" href="fdiff_1.html#T34">FDIFF_1:34</a>, <a class="ref" href="sin_cos.html#T72">SIN_COS:72</a></i>;<br/>
<i><font color="Green">E16</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="seq_1.html#K16">-</a> <a href="sin_cos.html#K19">sin</a> </span>)</span> <a href="partfun1.html#K2">|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="seq_1.html#K16">-</a> <a href="sin_cos.html#K19">sin</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span>
<b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="seq_1.html#K13">(#)</a> <a href="sin_cos.html#K19">sin</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T38">RFUNCT_1:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <a href="sin_cos.html#K19">sin</a> </span>)</span> <a href="subset_1.html#K9">/\</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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span>
<b>by </b><i><a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>
<br/>.= 
<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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a>, <a class="ref" href="sin_cos.html#T27">SIN_COS:27</a></i>
;<br/>
<i><font color="Green">E17</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K19">sin</a>  <a href="partfun1.html#K2">|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <a href="sin_cos.html#K19">sin</a> </span>)</span> <a href="subset_1.html#K9">/\</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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span>
<b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>
<br/>.= 
<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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a>, <a class="ref" href="sin_cos.html#T27">SIN_COS:27</a></i>
;<br/>
<i><font color="Green">E18</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22">cos</a>  <a href="partfun1.html#K2">|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <a href="sin_cos.html#K22">cos</a> </span>)</span> <a href="subset_1.html#K9">/\</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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span>
<b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>
<br/>.= 
<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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a>, <a class="ref" href="sin_cos.html#T27">SIN_COS:27</a></i>
;<br/>
<a NAME="E7:18"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>1</sub></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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span> holds <br/><span class="p1">(<span class="default"><a href="sin_cos.html#K19">sin</a>  <a href="fdiff_1.html#K2">`|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22">cos</a>  <a href="partfun1.html#K2">|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>

<b>assume </b><a NAME="E1:18_4"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>2</sub></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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span>
 ;<br/>

<span class="p1">(<span class="default"><a href="sin_cos.html#K19">sin</a>  <a href="fdiff_1.html#K2">`|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font> = 
 <a href="fdiff_1.html#K1">diff</a> <a href="sin_cos.html#K19">sin</a> ,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="fdiff_1.html#D8">FDIFF_1:def 8</a>, <a class="txt" href="taylor_2.html#E1:18"><i><font color="Green">E13</font></i></a>, <a class="txt" href="taylor_2.html#E1:18_4"><i><font color="Green">E20</font></i></a></i>
<br/>.= 
<a href="sin_cos.html#K22">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="sin_cos.html#T69">SIN_COS:69</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="sin_cos.html#K22">cos</a>  <a href="partfun1.html#K2">|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="funct_1.html#T70">FUNCT_1:70</a>, <a class="txt" href="taylor_2.html#E1:18_4"><i><font color="Green">E20</font></i></a>, <a class="txt" href="taylor_2.html#E6:18"><i><font color="Green">E18</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E3:18_4"/>
<span class="p1">(<span class="default"><a href="sin_cos.html#K19">sin</a>  <a href="fdiff_1.html#K2">`|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22">cos</a>  <a href="partfun1.html#K2">|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E8:18"/><i><font color="Green">E20</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22">cos</a>  <a href="fdiff_1.html#K2">`|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="hidden.html#R1">=</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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span>
 
<b>by </b><i><a class="ref" href="fdiff_1.html#D8">FDIFF_1:def 8</a>, <a class="txt" href="taylor_2.html#E3:18"><i><font color="Green">E15</font></i></a></i>;<br/>
<a NAME="E9:18"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>1</sub></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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span> holds <br/><span class="p1">(<span class="default"><a href="sin_cos.html#K22">cos</a>  <a href="fdiff_1.html#K2">`|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="seq_1.html#K16">-</a> <a href="sin_cos.html#K19">sin</a> </span>)</span> <a href="partfun1.html#K2">|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>

<b>assume </b><a NAME="E1:18_5"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>2</sub></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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span>
 ;<br/>

<a NAME="E2:18_5"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="sin_cos.html#K19">sin</a> 
 
<b>by </b><i><a class="ref" href="sin_cos.html#T27">SIN_COS:27</a></i>;<br/>
<a NAME="E3:18_5"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="seq_1.html#K13">(#)</a> <a href="sin_cos.html#K19">sin</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>;<br/>
<span class="p1">(<span class="default"><a href="sin_cos.html#K22">cos</a>  <a href="fdiff_1.html#K2">`|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font> = 
 <a href="fdiff_1.html#K1">diff</a> <a href="sin_cos.html#K22">cos</a> ,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="fdiff_1.html#D8">FDIFF_1:def 8</a>, <a class="txt" href="taylor_2.html#E3:18"><i><font color="Green">E15</font></i></a>, <a class="txt" href="taylor_2.html#E1:18_5"><i><font color="Green">E21</font></i></a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K19">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos.html#T68">SIN_COS:68</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K19">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="seq_1.html#K13">(#)</a> <a href="sin_cos.html#K19">sin</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a>, <a class="txt" href="taylor_2.html#E3:18_5"><i><font color="Green">E22</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="seq_1.html#K16">-</a> <a href="sin_cos.html#K19">sin</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="rfunct_1.html#T38">RFUNCT_1:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="seq_1.html#K16">-</a> <a href="sin_cos.html#K19">sin</a> </span>)</span> <a href="partfun1.html#K2">|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="funct_1.html#T70">FUNCT_1:70</a>, <a class="txt" href="taylor_2.html#E1:18_5"><i><font color="Green">E21</font></i></a>, <a class="txt" href="taylor_2.html#E4:18"><i><font color="Green">E16</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E5:18_5"/>
<span class="p1">(<span class="default"><a href="sin_cos.html#K22">cos</a>  <a href="fdiff_1.html#K2">`|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="seq_1.html#K16">-</a> <a href="sin_cos.html#K19">sin</a> </span>)</span> <a href="partfun1.html#K2">|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E10:18"/>
( <a href="sin_cos.html#K19">sin</a>  <a href="fdiff_1.html#K2">`|</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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="hidden.html#R1">=</a> <a href="sin_cos.html#K22">cos</a>  <a href="partfun1.html#K2">|</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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span> &amp; <a href="sin_cos.html#K22">cos</a>  <a href="fdiff_1.html#K2">`|</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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="seq_1.html#K16">-</a> <a href="sin_cos.html#K19">sin</a> </span>)</span> <a href="partfun1.html#K2">|</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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K19">sin</a>  <a href="partfun1.html#K2">|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="hidden.html#R1">=</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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K22">cos</a>  <a href="partfun1.html#K2">|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="hidden.html#R1">=</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> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K2">.[</a></span> )
 <b>by </b><i><a class="txt" href="taylor_2.html#E2:18"><i><font color="Green">E14</font></i></a>, <a class="txt" href="taylor_2.html#E4:18"><i><font color="Green">E16</font></i></a>, <a class="txt" href="taylor_2.html#E5:18"><i><font color="Green">E17</font></i></a>, <a class="txt" href="taylor_2.html#E6:18"><i><font color="Green">E18</font></i></a>, <a class="txt" href="taylor_2.html#E7:18"><i><font color="Green">E19</font></i></a>, <a class="txt" href="taylor_2.html#E8:18"><i><font color="Green">E20</font></i></a>, <a class="ref" href="partfun1.html#T34">PARTFUN1:34</a></i>;<br/>


</div>
