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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="csspace.html#NM1" title="CSSPACE:NM.1">ComplexUnitarySpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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">X</font><br/> for <font color="Olive" title="b3">z1</font>, <font color="Olive" title="b4">z2</font> being  <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b3">z1</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <span class="p2">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <font color="Olive" title="b1">seq1</font></span>)</span></span>)</span> <a href="csspace.html#K16" title="CSSPACE:func.16">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">z2</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <span class="p2">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <font color="Olive" title="b2">seq2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">z1</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Olive" title="b1">seq1</font></span>)</span> <a href="csspace.html#K16" title="CSSPACE:func.16">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">z2</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Olive" title="b2">seq2</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">seq1</font>, <font color="Maroon" title="c3">seq2</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">z1</font>, <font color="Olive" title="b2">z2</font> being  <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">z1</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <span class="p2">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <font color="Maroon" title="c2">seq1</font></span>)</span></span>)</span> <a href="csspace.html#K16" title="CSSPACE:func.16">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">z2</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <span class="p2">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <font color="Maroon" title="c3">seq2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">z1</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c2">seq1</font></span>)</span> <a href="csspace.html#K16" title="CSSPACE:func.16">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">z2</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c3">seq2</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">z1</font>, <font color="Maroon" title="c5">z2</font> be   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <span class="p2">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <font color="Maroon" title="c2">seq1</font></span>)</span></span>)</span> <a href="csspace.html#K16" title="CSSPACE:func.16">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <span class="p2">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <font color="Maroon" title="c3">seq2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c2">seq1</font></span>)</span> <a href="csspace.html#K16" title="CSSPACE:func.16">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c3">seq2</font></span>)</span></span>)</span></span><br/>









<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <span class="p2">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <font color="Maroon" title="c2">seq1</font></span>)</span></span>)</span> <a href="csspace.html#K16" title="CSSPACE:func.16">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <span class="p2">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <font color="Maroon" title="c3">seq2</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c2">seq1</font></span>)</span></span>)</span> <a href="csspace.html#K16" title="CSSPACE:func.16">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <span class="p2">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <font color="Maroon" title="c3">seq2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_3.html#T3" target="_self" title="CLVECT_3:th.3">Th3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c2">seq1</font></span>)</span></span>)</span> <a href="csspace.html#K16" title="CSSPACE:func.16">+</a> <span class="p1">(<span class="default"><a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c3">seq2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_3.html#T3" target="_self" title="CLVECT_3:th.3">Th3</a></span>
<br/>.= 
 <a href="bhsp_4.html#K1" title="BHSP_4:func.1">Partial_Sums</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c2">seq1</font></span>)</span> <a href="csspace.html#K16" title="CSSPACE:func.16">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c3">seq2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_3.html#T1" target="_self" title="CLVECT_3:th.1">Th1</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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