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<span class="kw">set </span><font color="Maroon" title="c1">W</font> =  <a href="csspace.html#K11" title="CSSPACE:func.11">the_set_of_l2ComplexSequences</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c2">L1</font> =  <a href="csspace.html#K7" title="CSSPACE:func.7">Linear_Space_of_ComplexSequences</a> ;<br/>
<span class="kw">let </span><font color="Maroon" title="c3">r</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">u</font> being   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="csspace.html#K18" title="CSSPACE:func.18">Complex_l2_Space</a> holds  <font color="Maroon" title="c3">r</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p1">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Olive" title="b1">u</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">u</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="csspace.html#K18" title="CSSPACE:func.18">Complex_l2_Space</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">r</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p1">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c4">u</font></span>)</span></span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c5">u1</font> = <font color="Maroon" title="c4">u</font> as   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="csspace.html#K7" title="CSSPACE:func.7">Linear_Space_of_ComplexSequences</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#T29" title="CLVECT_1:th.29">CLVECT_1:29</a>, <a class="ref" href="csspace.html#T13" title="CSSPACE:th.13">CSSPACE:13</a>, <a class="ref" href="csspace.html#D18" title="CSSPACE:def.18">CSSPACE:def 18</a></span>;<br/>
<a NAME="E2:14"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a>  the <a href="clvect_1.html#U1" title="CLVECT_1:sel.1">Mult</a> of <a href="csspace.html#K7" title="CSSPACE:func.7">Linear_Space_of_ComplexSequences</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="csspace.html#K7" title="CSSPACE:func.7">Linear_Space_of_ComplexSequences</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E3:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"> the <a href="clvect_1.html#U1" title="CLVECT_1:sel.1">Mult</a> of <a href="csspace.html#K7" title="CSSPACE:func.7">Linear_Space_of_ComplexSequences</a> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>,<a href="csspace.html#K11" title="CSSPACE:func.11">the_set_of_l2ComplexSequences</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>,<a href="csspace.html#K11" title="CSSPACE:func.11">the_set_of_l2ComplexSequences</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T62" title="RELAT_1:th.62">RELAT_1:62</a>, <a class="ref" href="zfmisc_1.html#T96" title="ZFMISC_1:th.96">ZFMISC_1:96</a></span>;<br/>
<font color="Maroon" title="c3">r</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c4">u</font> = 
 the <a href="clvect_1.html#U1" title="CLVECT_1:sel.1">Mult</a> of <a href="csspace.html#K18" title="CSSPACE:func.18">Complex_l2_Space</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c4">u</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#D1" title="CLVECT_1:def.1">CLVECT_1:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"> the <a href="clvect_1.html#U1" title="CLVECT_1:sel.1">Mult</a> of <a href="csspace.html#K7" title="CSSPACE:func.7">Linear_Space_of_ComplexSequences</a> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>,<a href="csspace.html#K11" title="CSSPACE:func.11">the_set_of_l2ComplexSequences</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c4">u</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="csspace.html#T12" title="CSSPACE:th.12">CSSPACE:12</a>, <a class="ref" href="csspace.html#D9" title="CSSPACE:def.9">CSSPACE:def 9</a>, <a class="ref" href="csspace.html#D18" title="CSSPACE:def.18">CSSPACE:def 18</a></span>
<br/>.= 
 the <a href="clvect_1.html#U1" title="CLVECT_1:sel.1">Mult</a> of <a href="csspace.html#K7" title="CSSPACE:func.7">Linear_Space_of_ComplexSequences</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c4">u</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="csspace.html#D18" title="CSSPACE:def.18">CSSPACE:def 18</a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>
<br/>.= 
<font color="Maroon" title="c3">r</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">u1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#D1" title="CLVECT_1:def.1">CLVECT_1:def 1</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:14"/>
<font color="Maroon" title="c3">r</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p1">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c4">u</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="csspace.html#T15" title="CSSPACE:th.15">CSSPACE:15</a></span>; <a class="txt" 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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