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<b>let </b><font color="Maroon">seq</font> be   <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/><b>let </b><font color="Maroon">h</font> be   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K2">COMPLEX</a> , <a href="numbers.html#K2">COMPLEX</a> ;<br/><b>let </b><font color="Maroon">Ns</font> be  <a href="seqm_3.html#V1">increasing</a> <a href="seqm_3.html#NM1">Seq_of_Nat</a>;<br/>





<b>assume </b><a NAME="E1:24"/><i><font color="Green">E53</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">seq</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">h</font>
 ;<br/>

<a NAME="E2:24"/><b>then </b><i><font color="Green">E55</font></i>: 
 <a href="comseq_3.html#K3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="cfcont_1.html#K1" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="comseq_3.html#K5">*</a> <font color="Maroon">Ns</font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="comseq_3.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="cfcont_1.html#K1" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="comseq_3.html#K5">*</a> <font color="Maroon">Ns</font></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E3:24"/>
 <a href="comseq_3.html#K4">Im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="cfcont_1.html#K1" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="comseq_3.html#K5">*</a> <font color="Maroon">Ns</font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="comseq_3.html#K4">Im</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="cfcont_1.html#K1" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="comseq_3.html#K5">*</a> <font color="Maroon">Ns</font></span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:24"/>
<span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="cfcont_1.html#K1" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="comseq_3.html#K5">*</a> <font color="Maroon">Ns</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">h</font> <a href="cfcont_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="comseq_3.html#K5">*</a> <font color="Maroon">Ns</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="comseq_3.html#T14">COMSEQ_3:14</a></i>;<br/>


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