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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">u</font>, <font color="Maroon" title="c4">v</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="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">u</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p1">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c4">v</font></span>)</span></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">u1</font> = <font color="Maroon" title="c3">u</font>, <font color="Maroon" title="c6">v1</font> = <font color="Maroon" title="c4">v</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#T30" title="CLVECT_1:th.30">CLVECT_1:30</a>, <a class="ref" href="csspace.html#T15" title="CSSPACE:th.15">CSSPACE:15</a>, <a class="ref" href="csspace.html#D20" title="CSSPACE:def.20">CSSPACE:def 20</a></span>;<br/>
<a NAME="E2:13"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</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">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> ,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="E3:13"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">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="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <a href="csspace.html#K7" title="CSSPACE:func.7">Linear_Space_of_ComplexSequences</a>  <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <a href="csspace.html#K11" title="CSSPACE:func.11">the_set_of_l2ComplexSequences</a> </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="csspace.html#K11" title="CSSPACE:func.11">the_set_of_l2ComplexSequences</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#T91" title="RELAT_1:th.91">RELAT_1:91</a>, <a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</a></span>;<br/>
<font color="Maroon" title="c3">u</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">v</font> = 
<span class="p1">(<span class="default">the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <a href="csspace.html#K7" title="CSSPACE:func.7">Linear_Space_of_ComplexSequences</a>  <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <a href="csspace.html#K11" title="CSSPACE:func.11">the_set_of_l2ComplexSequences</a> </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">u</font>,<font color="Maroon" title="c4">v</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#T14" title="CSSPACE:th.14">CSSPACE:14</a>, <a class="ref" href="csspace.html#D8" title="CSSPACE:def.8">CSSPACE:def 8</a>, <a class="ref" href="csspace.html#D20" title="CSSPACE:def.20">CSSPACE:def 20</a></span>
<br/>.= 
<font color="Maroon" title="c5">u1</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">v1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="csspace.html#D20" title="CSSPACE:def.20">CSSPACE:def 20</a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:13"/>
<font color="Maroon" title="c3">u</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c3">u</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p1">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c4">v</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="csspace.html#T17" title="CSSPACE:th.17">CSSPACE:17</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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