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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ,   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a>  = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="sin_cos.html#K7" target="_self">ExpSeq</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">a<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="series_1.html#K1">Partial_Sums</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="sin_cos.html#K7" target="_self">ExpSeq</a> </span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="series_1.html#K1">Partial_Sums</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="sin_cos.html#K7" target="_self">ExpSeq</a> </span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="binarith.html#K3">-'</a> <font color="Maroon">a<sub>2</sub></font></span>)</span></span>)</span></span>)</span>;<br/>
<a NAME="E1:19_1_1"/>
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   ex <font color="Olive">rseq</font> being  <a href="seq_1.html#NM1">Real_Sequence</a> st <br/>for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds <br/> ( ( <font color="Olive">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">n</font> implies <font color="Olive">rseq</font> <a href="seq_1.html#K2">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">n</font>,<font color="Olive">k</font>) ) &amp; ( <font color="Olive">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Olive">n</font> implies <font color="Olive">rseq</font> <a href="seq_1.html#K2">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> 0 ) )
 
<b>from </b><i><a class="ref" href="sin_cos.html#S2" target="_self">SIN_COS:sch 2</a>();<br/></i>
<b>hence </b><a NAME="E2:19_1_1"/>
 ex <font color="Olive">rseq</font> being  <a href="seq_1.html#NM1">Real_Sequence</a> st <br/>for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds <br/> ( ( <font color="Olive">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> implies <font color="Olive">rseq</font> <a href="seq_1.html#K2">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="sin_cos.html#K7" target="_self">ExpSeq</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">k</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="series_1.html#K1">Partial_Sums</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="sin_cos.html#K7" target="_self">ExpSeq</a> </span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="series_1.html#K1">Partial_Sums</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="sin_cos.html#K7" target="_self">ExpSeq</a> </span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="binarith.html#K3">-'</a> <font color="Olive">k</font></span>)</span></span>)</span></span>)</span> ) &amp; ( <font color="Olive">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">n</font> implies <font color="Olive">rseq</font> <a href="seq_1.html#K2">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> 0 ) )
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