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<span class="kw">let </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> be   <a href="xcmplx_0.html#NM1" title="XCMPLX_0:NM.1">Complex</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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">seq</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Olive" title="b1">X</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="clvect_1.html#K6" title="CLVECT_1:func.6">*</a> <font color="Olive" title="b2">seq</font> <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#K6" title="CLVECT_1:func.6">*</a> <font color="Olive" title="b2">seq</font></span>)</span> <a href="csspace.html#K14" title="CSSPACE:func.14">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="clvect_1.html#K6" title="CLVECT_1:func.6">*</a> <font color="Olive" title="b2">seq</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">X</font> be   <a href="csspace.html#NM1" title="CSSPACE:NM.1">ComplexUnitarySpace</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">seq</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c6">X</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="clvect_1.html#K6" title="CLVECT_1:func.6">*</a> <font color="Olive" title="b1">seq</font> <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#K6" title="CLVECT_1:func.6">*</a> <font color="Olive" title="b1">seq</font></span>)</span> <a href="csspace.html#K14" title="CSSPACE:func.14">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="clvect_1.html#K6" title="CLVECT_1:func.6">*</a> <font color="Olive" title="b1">seq</font></span>)</span></span><br/><span class="kw">let </span><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="c6">X</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="clvect_1.html#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font> <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#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font></span>)</span> <a href="csspace.html#K14" title="CSSPACE:func.14">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="clvect_1.html#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font></span>)</span></span><br/>







<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="93_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="clvect_1.html#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b1">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#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font></span>)</span> <a href="csspace.html#K14" title="CSSPACE:func.14">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="clvect_1.html#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font></span>)</span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b1">n</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="clvect_1.html#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</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#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font></span>)</span> <a href="csspace.html#K14" title="CSSPACE:func.14">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="clvect_1.html#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font></span>)</span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="clvect_1.html#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">seq</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#D14" onmouseover="rs('clvect_1/D14')" onmouseout="rh()">CLVECT_1:def 14</a></span>
<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="c7">seq</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</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="c5">b</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">seq</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#D3" onmouseover="rs('clvect_1/D3')" onmouseout="rh()">CLVECT_1:def 3</a></span>
<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#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</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="c5">b</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">seq</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#D14" onmouseover="rs('clvect_1/D14')" onmouseout="rh()">CLVECT_1:def 14</a></span>
<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#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</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"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="clvect_1.html#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#D14" onmouseover="rs('clvect_1/D14')" onmouseout="rh()">CLVECT_1:def 14</a></span>
<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#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font></span>)</span> <a href="csspace.html#K14" title="CSSPACE:func.14">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="clvect_1.html#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font></span>)</span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="normsp_1.html#D2" onmouseover="rs('normsp_1/D2')" onmouseout="rh()">NORMSP_1:def 2</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:93"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="clvect_1.html#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font> <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#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font></span>)</span> <a href="csspace.html#K14" title="CSSPACE:func.14">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="clvect_1.html#K6" title="CLVECT_1:func.6">*</a> <font color="Maroon" title="c7">seq</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T63" onmouseover="rs('funct_2/T63')" onmouseout="rh()">FUNCT_2:63</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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