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<b>let </b><font color="Maroon" title="c1">g</font> be    <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> ;<br/><b>let </b><font color="Maroon" title="c2">seq</font> be   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a>;<br/><b>let </b><font color="Maroon" title="c3">Ns</font> be  <a href="seqm_3.html#V1" title="SEQM_3:attr.1">increasing</a> <a href="seqm_3.html#NM1" title="SEQM_3:NM.1">Seq_of_Nat</a>;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">n</font> be    <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> ;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="comseq_1.html#K4" title="COMSEQ_1:func.4">(#)</a> <font color="Maroon" title="c2">seq</font></span>)</span> <a href="comseq_3.html#K5" title="COMSEQ_3:func.5">*</a> <font color="Maroon" title="c3">Ns</font></span>)</span> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <font color="Maroon" title="c4">n</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="comseq_1.html#K4" title="COMSEQ_1:func.4">(#)</a> <font color="Maroon" title="c2">seq</font></span>)</span> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Ns</font> <a href="seqm_3.html#K2" title="SEQM_3:func.2">.</a> <font color="Maroon" title="c4">n</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
<br/>.= 
<font color="Maroon" title="c1">g</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</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="Maroon" title="c3">Ns</font> <a href="seqm_3.html#K2" title="SEQM_3:func.2">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_1.html#D7" title="COMSEQ_1:def.7">COMSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon" title="c1">g</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="comseq_3.html#K5" title="COMSEQ_3:func.5">*</a> <font color="Maroon" title="c3">Ns</font></span>)</span> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <font color="Maroon" title="c4">n</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="comseq_1.html#K4" title="COMSEQ_1:func.4">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="comseq_3.html#K5" title="COMSEQ_3:func.5">*</a> <font color="Maroon" title="c3">Ns</font></span>)</span></span>)</span> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <font color="Maroon" title="c4">n</font>
<b>by </b><i><a class="ref" href="comseq_1.html#D7" title="COMSEQ_1:def.7">COMSEQ_1:def 7</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:10"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="comseq_1.html#K4" title="COMSEQ_1:func.4">(#)</a> <font color="Maroon" title="c2">seq</font></span>)</span> <a href="comseq_3.html#K5" title="COMSEQ_3:func.5">*</a> <font color="Maroon" title="c3">Ns</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c1">g</font> <a href="comseq_1.html#K4" title="COMSEQ_1:func.4">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="comseq_3.html#K5" title="COMSEQ_3:func.5">*</a> <font color="Maroon" title="c3">Ns</font></span>)</span>
 <b>by </b><i><a class="ref" href="comseq_1.html#T6" title="COMSEQ_1:th.6">COMSEQ_1:6</a></i>;<br/>


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