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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#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a>  = <font color="Maroon">seq</font> <a href="comseq_1.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> , <a href="numbers.html#K2">COMPLEX</a> <b> such that </b><br/><a NAME="E2:15_1_1"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">f</font> <a href="comseq_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a>  <a href="complex1.html#K5">0c</a>  &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">f</font> <a href="comseq_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">n</font>,<font color="Maroon">f</font> <a href="comseq_1.html#K1">.</a> <font color="Olive">n</font>) ) )
 <b>from </b><i><a class="ref" href="recdef_1.html#S4">RECDEF_1:sch 4</a>();<br/></i>
<b>reconsider </b><font color="Maroon">f</font> = <font color="Maroon">f</font> as   <a href="comseq_1.html#NM1">Complex_Sequence</a> ;<br/>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>thus </b><a NAME="E4:15_1_1"/>
( <font color="Maroon">f</font> <a href="comseq_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> 0 &amp; ( for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">f</font> <a href="comseq_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">seq</font> <a href="comseq_1.html#K1">.</a> <font color="Olive">k</font> ) )
 <b>by </b><i/>;<br/>


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