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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>; <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>, <font color="Olive" title="b3">seq3</font> being  <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c4">X</font> holds  <font color="Olive" title="b1">seq1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">seq2</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Olive" title="b3">seq3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">seq1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Olive" title="b2">seq2</font></span>)</span> <a href="bhsp_1.html#K8" title="BHSP_1:func.8">+</a> <font color="Olive" title="b3">seq3</font></span><br/><b>let </b><font color="Maroon" title="c5">seq1</font>, <font color="Maroon" title="c6">seq2</font>, <font color="Maroon" title="c7">seq3</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c4">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">seq1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">seq2</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">seq3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><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></span>)</span> <a href="bhsp_1.html#K8" title="BHSP_1:func.8">+</a> <font color="Maroon" title="c7">seq3</font></span><br/>







<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c5">seq1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">seq2</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">seq3</font></span>)</span></span>)</span> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c8">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><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></span>)</span> <a href="bhsp_1.html#K8" title="BHSP_1:func.8">+</a> <font color="Maroon" title="c7">seq3</font></span>)</span> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c8">n</font></span><br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c5">seq1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">seq2</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">seq3</font></span>)</span></span>)</span> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c8">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="c8">n</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">seq2</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">seq3</font></span>)</span> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c8">n</font></span>)</span>
<b>by </b><i><a class="ref" href="normsp_1.html#D6" title="NORMSP_1:def.6">NORMSP_1:def 6</a></i>
<br/>.= 
<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="c8">n</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<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="c8">n</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">seq3</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="normsp_1.html#D6" title="NORMSP_1:def.6">NORMSP_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<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="c8">n</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<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="c8">n</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">seq3</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c8">n</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T43" title="RLVECT_1:th.43">RLVECT_1:43</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><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></span>)</span> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c8">n</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">seq3</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c8">n</font></span>)</span>
<b>by </b><i><a class="ref" href="normsp_1.html#D6" title="NORMSP_1:def.6">NORMSP_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><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></span>)</span> <a href="bhsp_1.html#K8" title="BHSP_1:func.8">+</a> <font color="Maroon" title="c7">seq3</font></span>)</span> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c8">n</font>
<b>by </b><i><a class="ref" href="normsp_1.html#D5" title="NORMSP_1:def.5">NORMSP_1:def 5</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:76"/>
<font color="Maroon" title="c5">seq1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">seq2</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">seq3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><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></span>)</span> <a href="bhsp_1.html#K8" title="BHSP_1:func.8">+</a> <font color="Maroon" title="c7">seq3</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</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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