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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="nat_1.html#NM1">Nat</a>,  <a href="nat_1.html#NM1">Nat</a>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a>  = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K8" target="_self">Coef</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="comseq_1.html#K1">.</a> <font color="Maroon">a<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_3.html#K2">#N</a> <font color="Maroon">a<sub>2</sub></font></span>)</span></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="comseq_3.html#K2">#N</a> <span class="p2">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">a<sub>2</sub></font></span>)</span></span>)</span>;<br/>
<a NAME="E1:16_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a>ex <font color="Olive">b<sub>2</sub></font> being  <a href="comseq_1.html#NM1">Complex_Sequence</a> st <br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <br/>( ( <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> implies <font color="Olive">b<sub>2</sub></font> <a href="comseq_1.html#K1">.</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font>) ) &amp; ( <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Olive">b<sub>1</sub></font> implies <font color="Olive">b<sub>2</sub></font> <a href="comseq_1.html#K1">.</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 ) )
 
<b>from </b><i><a class="ref" href="sin_cos.html#S1" target="_self">SIN_COS:sch 1</a>();<br/></i>
<b>hence </b><a NAME="E2:16_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="comseq_1.html#NM1">Complex_Sequence</a> st <br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <br/>( ( <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="comseq_1.html#K1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K8" target="_self">Coef</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="comseq_1.html#K1">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="comseq_1.html#K1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 ) )
 ;<br/>


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