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<b>let </b><font color="Maroon" title="c4">X</font> be   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon" title="c5">seq1</font>, <font color="Maroon" title="c6">seq2</font>, <font color="Maroon" title="c7">seq</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c4">X</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:58"/><i><font color="Green" title="E31">A1</font></i>: 
<font color="Maroon" title="c5">seq1</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 <b>and </b><br/><a NAME="E2:58"/><i><font color="Green" title="E32">A2</font></i>: 
<font color="Maroon" title="c6">seq2</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 <b>and </b><br/><a NAME="E3:58"/><i><font color="Green" title="E33">A3</font></i>: 
<font color="Maroon" title="c7">seq</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">seq1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c6">seq2</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c8">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">X</font><b> such that </b><br/><a NAME="E5:58"/><i><font color="Green" title="E34">A4</font></i>: 
for <font color="Olive" title="b1">n</font> being   <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>  holds  <font color="Maroon" title="c5">seq1</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">x</font>
 <b>by </b><i><a class="txt" href="bhsp_1.html#E1:58"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="normsp_1.html#D4" title="NORMSP_1:def.4">NORMSP_1:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">X</font><b> such that </b><br/><a NAME="E7:58"/><i><font color="Green" title="E35">A5</font></i>: 
for <font color="Olive" title="b1">n</font> being   <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>  holds  <font color="Maroon" title="c6">seq2</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">y</font>
 <b>by </b><i><a class="txt" href="bhsp_1.html#E2:58"><i><font color="Green" title="E32">A2</font></i></a>, <a class="ref" href="normsp_1.html#D4" title="NORMSP_1:def.4">NORMSP_1:def 4</a></i>;<br/>
<b>take </b><font color="Maroon" title="c10">z</font> = <font color="Maroon" title="c8">x</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c9">y</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="normsp_1.html#D4" title="NORMSP_1:def.4">NORMSP_1:def 4</a><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c11">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><font color="Maroon" title="c7">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c11">n</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">seq1</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c11">n</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">seq2</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c11">n</font></span>)</span>
<b>by </b><i><a class="txt" href="bhsp_1.html#E3:58"><i><font color="Green" title="E33">A3</font></i></a>, <a class="ref" href="normsp_1.html#D6" title="NORMSP_1:def.6">NORMSP_1:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c8">x</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">seq2</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c11">n</font></span>)</span>
<b>by </b><i><a class="txt" href="bhsp_1.html#E5:58"><i><font color="Green" title="E34">A4</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c10">z</font>
<b>by </b><i><a class="txt" href="bhsp_1.html#E7:58"><i><font color="Green" title="E35">A5</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E9:58"/>
for <font color="Olive">b<sub>1</sub></font> being   <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>  holds  <a href="seq_1.html#K2" title="SEQ_1:func.2">K184</a>(the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c7">seq</font>,<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">z</font>
 ;<br/>


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