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<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>

<span class="p1">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p3">(<span class="default"><span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>3</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K6" target="_self">ExpSeq</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos.html#D20" target="_self">Def20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p3">(<span class="default"><span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default">0,<span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K6" target="_self">ExpSeq</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p3">(<span class="default"><span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>3</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K6" target="_self">ExpSeq</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos.html#D20" target="_self">Def20</a></i>
<br/>.= 
 <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p3">(<span class="default"><span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p5">(<span class="default">0 <a href="nat_1.html#K1">+</a> 0</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K6" target="_self">ExpSeq</a> </span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p3">(<span class="default"><span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>3</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K6" target="_self">ExpSeq</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T48">COMPLEX1:48</a></i>
<br/>.= 
 <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>3</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K8">+</a> <span class="p5"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span></span>)</span> <a href="sin_cos.html#K6" target="_self">ExpSeq</a> </span>)</span></span>)</span> <a href="complex1.html#K11">-</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p3">(<span class="default"><span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>3</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K6" target="_self">ExpSeq</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sin_cos.html#E82"><i><font color="Green">Lemma62</font></i></a></i>
<br/>.= 
 <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p4">(<span class="default"><span class="p5"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>3</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K6" target="_self">ExpSeq</a> </span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p5">(<span class="default"><span class="p0"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K30" target="_self">P_dt</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p4">(<span class="default"><span class="p5"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>3</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K6" target="_self">ExpSeq</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sin_cos.html#T64" target="_self">Th64</a></i>
<br/>.= 
 <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p5">(<span class="default"><span class="p0"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K30" target="_self">P_dt</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p4">(<span class="default"><span class="p5"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>3</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K6" target="_self">ExpSeq</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sin_cos.html#E54"><i><font color="Green">Lemma42</font></i></a></i>
<br/>.= 
 <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K9">*</a> <span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p5">(<span class="default"><span class="p0"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K30" target="_self">P_dt</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p4">(<span class="default"><span class="p5"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>3</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K6" target="_self">ExpSeq</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T27">COMPLEX1:27</a></i>
<br/>.= 
 <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K9">*</a> <span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p5">(<span class="default"><span class="p0"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K30" target="_self">P_dt</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sin_cos.html#E54"><i><font color="Green">Lemma42</font></i></a></i>
<br/>.= 
 <a href="complex1.html#K4">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K9">*</a> <span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p5">(<span class="default"><span class="p0"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K30" target="_self">P_dt</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T27">COMPLEX1:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p2">(<span class="default"><span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K9">*</a> <span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p5">(<span class="default"><span class="p0"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K30" target="_self">P_dt</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T19">COMPLEX1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p2"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span><a href="arytm_0.html#K5">*]</a></span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p5">(<span class="default"><span class="p0"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K30" target="_self">P_dt</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sin_cos.html#E68"><i><font color="Green">Lemma51</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K9">*</a> <span class="p4">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p5">(<span class="default"><span class="p0"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K30" target="_self">P_dt</a> </span>)</span></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p4">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T27">COMPLEX1:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p2">(<span class="default"><span class="p3"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="complex1.html#K9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p5">(<span class="default"><span class="p0"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K30" target="_self">P_dt</a> </span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p5">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p5">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T28">COMPLEX1:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p5">(<span class="default"><span class="p0"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K30" target="_self">P_dt</a> </span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p5">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p5">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="sin_cos.html#E110"><i><font color="Green">Lemma83</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E2:109"/>
<span class="p1">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="comseq_3.html#K8">Sum</a> <span class="p5">(<span class="default"><span class="p0"><a href="arytm_0.html#K5">[*</a><span class="default">0,<font color="Maroon">c<sub>4</sub></font></span><a href="arytm_0.html#K5">*]</a></span> <a href="sin_cos.html#K30" target="_self">P_dt</a> </span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p4"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p5">(<span class="default"><a href="sin_cos.html#K22" target="_self">cos</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p5">(<span class="default"><a href="sin_cos.html#K19" target="_self">sin</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="arytm_0.html#K5">*]</a></span></span>)</span></span>)</span></span>)</span>
 ;<br/>


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