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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ) <b>-&gt; </b>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  = $2 <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <span class="p2">(<span class="default">$1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c3">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> <b> such that </b><br/><a NAME="E2:33_1_1"/><i><font color="Green" title="E19">A1</font></i>: 
( <font color="Maroon" title="c3">f</font> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">seq</font> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; ( for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c3">f</font> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">n</font>,<font color="Maroon" title="c3">f</font> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <font color="Olive" title="b1">n</font>) ) )
 <b>from </b><i><a class="ref" href="recdef_1.html#S4" title="RECDEF_1:sch.4">RECDEF_1:sch 4</a>();<br/></i>
<b>take </b>
<font color="Maroon" title="c3">f</font>
;<br/>

<b>thus </b><a NAME="E3:33_1_1"/>
( <font color="Maroon" title="c3">f</font> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">seq</font> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; ( for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c3">f</font> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="comseq_3.html#E2:33_1_1"><i><font color="Green" title="E19">A1</font></i></a></i>;<br/>


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