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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="clvect_1.html#NM5">ComplexNormSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nfcont_1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:43"/><i><font color="Green">E41</font></i>: 
(  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> is    <a href="bhsp_3.html#M1">subsequence</a> of <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>6</sub></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="E3:43"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="lopban_3.html#K5">*</a> <font color="Maroon">c<sub>6</sub></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">c<sub>6</sub></font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="bhsp_3.html#D4">BHSP_3:def 4</a><br/>

<b>thus </b><a NAME="E4:43"/>
<font color="Maroon">c<sub>3</sub></font> <a href="ncfcont1.html#K6" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ncfcont1.html#K6" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ncfcont1.html#E1:43"><i><font color="Green">E41</font></i></a>, <a class="txt" href="ncfcont1.html#E3:43"><i><font color="Green">E42</font></i></a>, <a class="ref" href="ncfcont1.html#T17" target="_self">Th17</a></i>;<br/>


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