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<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">h</font> being  <a href="struct_0.html#NM10" title="STRUCT_0:NM.10">PartFunc</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font><br/> for <font color="Olive" title="b2">seq1</font>, <font color="Olive" title="b3">seq2</font> being  <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">S</font>  st  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Olive" title="b2">seq1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Olive" title="b1">h</font> &amp; <font color="Olive" title="b3">seq2</font> is    <a href="bhsp_3.html#M1" title="BHSP_3:mode.1">subsequence</a> of <font color="Olive" title="b2">seq1</font> holds <br/><font color="Olive" title="b1">h</font> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Olive" title="b3">seq2</font> is    <a href="bhsp_3.html#M1" title="BHSP_3:mode.1">subsequence</a> of <font color="Olive" title="b1">h</font> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Olive" title="b2">seq1</font></span><br/><b>let </b><font color="Maroon" title="c3">h</font> be   <a href="struct_0.html#NM10" title="STRUCT_0:NM.10">PartFunc</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">seq1</font>, <font color="Olive" title="b2">seq2</font> being  <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">S</font>  st  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Olive" title="b1">seq1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</font> &amp; <font color="Olive" title="b2">seq2</font> is    <a href="bhsp_3.html#M1" title="BHSP_3:mode.1">subsequence</a> of <font color="Olive" title="b1">seq1</font> holds <br/><font color="Maroon" title="c3">h</font> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Olive" title="b2">seq2</font> is    <a href="bhsp_3.html#M1" title="BHSP_3:mode.1">subsequence</a> of <font color="Maroon" title="c3">h</font> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Olive" title="b1">seq1</font></span><br/><b>let </b><font color="Maroon" title="c4">seq1</font>, <font color="Maroon" title="c5">seq2</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">seq1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</font> &amp; <font color="Maroon" title="c5">seq2</font> is    <a href="bhsp_3.html#M1" title="BHSP_3:mode.1">subsequence</a> of <font color="Maroon" title="c4">seq1</font> implies <font color="Maroon" title="c3">h</font> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Maroon" title="c5">seq2</font> is    <a href="bhsp_3.html#M1" title="BHSP_3:mode.1">subsequence</a> of <font color="Maroon" title="c3">h</font> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Maroon" title="c4">seq1</font> )</span><br/>







<b>assume </b><a NAME="E1:21"/><i><font color="Green" title="E19">A1</font></i>: 
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">seq1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</font> &amp; <font color="Maroon" title="c5">seq2</font> is    <a href="bhsp_3.html#M1" title="BHSP_3:mode.1">subsequence</a> of <font color="Maroon" title="c4">seq1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">h</font> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Maroon" title="c5">seq2</font> is    <a href="bhsp_3.html#M1" title="BHSP_3:mode.1">subsequence</a> of <font color="Maroon" title="c3">h</font> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Maroon" title="c4">seq1</font></span><br/>

<b>then consider </b><font color="Maroon" title="c6">Ns</font> being  <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><b> such that </b><br/><a NAME="E3:21"/><i><font color="Green" title="E20">A2</font></i>: 
<font color="Maroon" title="c5">seq2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">seq1</font> <a href="lopban_3.html#K4" title="LOPBAN_3:func.4">*</a> <font color="Maroon" title="c6">Ns</font>
 <b>by </b><i><a class="ref" href="bhsp_3.html#D4" title="BHSP_3:def.4">BHSP_3:def 4</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">Ns</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="bhsp_3.html#D4" title="BHSP_3:def.4">BHSP_3:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">h</font> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Maroon" title="c5">seq2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">Ns</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Maroon" title="c4">seq1</font></span>)</span></span><br/>

<b>thus </b><a NAME="E4:21"/>
<font color="Maroon" title="c3">h</font> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Maroon" title="c5">seq2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">Ns</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Maroon" title="c4">seq1</font></span>)</span>
 <b>by </b><i><a class="txt" href="nfcont_1.html#E1:21"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="nfcont_1.html#E3:21"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="nfcont_1.html#T10" target="_self" title="NFCONT_1:th.10">Th10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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