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<b>let </b><font color="Maroon">RNS</font> be   <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">h</font> be   <a href="partfun1.html#NM1">PartFunc</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">RNS</font>, <a href="numbers.html#K2">COMPLEX</a> ;<br/><b>let </b><font color="Maroon">Rseq1</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">RNS</font>, <font color="Maroon">Rseq2</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">RNS</font>;<br/>





<b>assume </b><a NAME="E1:48"/><i><font color="Green">E34</font></i>: 
(  <a href="relset_1.html#K5">rng</a> <font color="Maroon">Rseq1</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">h</font> &amp; <font color="Maroon">Rseq2</font> is    <a href="bhsp_3.html#M1">subsequence</a> of <font color="Maroon">Rseq1</font> )
 ;<br/>

<b>then consider </b><font color="Maroon">Ns</font> being  <a href="seqm_3.html#V1">increasing</a> <a href="seqm_3.html#NM1">Seq_of_Nat</a><b> such that </b><br/><a NAME="E3:48"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">Rseq2</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">Rseq1</font> <a href="lopban_3.html#K5">*</a> <font color="Maroon">Ns</font>
 <b>by </b><i><a class="ref" href="bhsp_3.html#D4">BHSP_3:def 4</a></i>;<br/>
<b>take </b>
<font color="Maroon">Ns</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="comseq_3.html#D9">COMSEQ_3:def 9</a><br/>

<a NAME="E4:48"/><i><font color="Green">E54</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="ncfcont1.html#K9" target="_self">*</a> <font color="Maroon">Rseq1</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="ncfcont1.html#K9" target="_self">*</a> <font color="Maroon">Rseq2</font>
 
<b>by </b><i>, <a class="ref" href="ncfcont1.html#D3" target="_self">Def3</a>, <a class="ref" href="ncfcont1.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E5:48"/>
<font color="Maroon">h</font> <a href="ncfcont1.html#K9" target="_self">*</a> <font color="Maroon">Rseq2</font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="ncfcont1.html#K9" target="_self">*</a> <font color="Maroon">Rseq1</font></span>)</span> <a href="comseq_3.html#K5">*</a> <font color="Maroon">Ns</font>
 
<b>by </b><i><a class="ref" href="ncfcont1.html#D4" target="_self">Def4</a></i>;<br/>
<b>hence </b><a NAME="E6:48"/>
<font color="Maroon">h</font> <a href="ncfcont1.html#K9" target="_self">*</a> <font color="Maroon">Rseq2</font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="ncfcont1.html#K9" target="_self">*</a> <font color="Maroon">Rseq1</font></span>)</span> <a href="comseq_3.html#K5">*</a> <font color="Maroon">Ns</font>
 ;<br/>


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