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<b>let </b><font color="Maroon" title="c4">a</font> be   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</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">X</font> being  <a href="csspace.html#NM1" title="CSSPACE:NM.1">ComplexUnitarySpace</a><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="Olive" title="b1">X</font> holds  <font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">seq1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Olive" title="b3">seq2</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="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Olive" title="b2">seq1</font></span>)</span> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Olive" title="b3">seq2</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c5">X</font> be   <a href="csspace.html#NM1" title="CSSPACE:NM.1">ComplexUnitarySpace</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> being  <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c5">X</font> holds  <font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</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="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Olive" title="b1">seq1</font></span>)</span> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Olive" title="b2">seq2</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c6">seq1</font>, <font color="Maroon" title="c7">seq2</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c5">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="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">seq1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">seq2</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="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c6">seq1</font></span>)</span> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c7">seq2</font></span>)</span></span><br/>







<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="108_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="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">seq1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">seq2</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="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c6">seq1</font></span>)</span> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c7">seq2</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><br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">seq1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">seq2</font></span>)</span></span>)</span> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c8">n</font> = 
<font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">seq1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">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>
<b>by </b><i><a class="ref" href="clvect_1.html#D15" title="CLVECT_1:def.15">CLVECT_1:def 15</a></i>
<br/>.= 
<font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">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="c7">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>
<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="c4">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">seq1</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#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">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>
<b>by </b><i><a class="ref" href="clvect_1.html#T10" title="CLVECT_1:th.10">CLVECT_1:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c6">seq1</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#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">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>
<b>by </b><i><a class="ref" href="clvect_1.html#D15" title="CLVECT_1:def.15">CLVECT_1:def 15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c6">seq1</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#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c7">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>
<b>by </b><i><a class="ref" href="clvect_1.html#D15" title="CLVECT_1:def.15">CLVECT_1:def 15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c6">seq1</font></span>)</span> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c7">seq2</font></span>)</span></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#D6" title="NORMSP_1:def.6">NORMSP_1:def 6</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="E2:108"/>
<font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">seq1</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <font color="Maroon" title="c7">seq2</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="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c6">seq1</font></span>)</span> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c7">seq2</font></span>)</span>
 <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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