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<b>let </b><font color="Maroon" title="c1">z</font> be   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a>;<br/><b>let </b><font color="Maroon" title="c2">v</font>, <font color="Maroon" title="c3">w</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <a href="csspace.html#K1" title="CSSPACE:func.1">the_set_of_ComplexSequences</a> ,<a href="csspace.html#K6" title="CSSPACE:func.6">CZeroseq</a> ,<a href="csspace.html#K4" title="CSSPACE:func.4">l_add</a> ,<a href="csspace.html#K5" title="CSSPACE:func.5">l_mult</a>  #);<br/>



<i><font color="Green" title="E15">A1</font></i>: <font color="Maroon" title="c1">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">w</font></span>)</span> = 
<font color="Maroon" title="c1">z</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> <span class="p2">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="csspace.html#T5" target="_self" title="CSSPACE:th.5">Th5</a></i>
<br/>.= 
<font color="Maroon" title="c1">z</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> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p3">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="csspace.html#D4" target="_self" title="CSSPACE:def.4">Def4</a></i>
<br/>.= 
<font color="Maroon" title="c1">z</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p2">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="csspace.html#T3" target="_self" title="CSSPACE:th.3">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c2">v</font></span>)</span></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_1.html#T19" title="COMSEQ_1:th.19">COMSEQ_1:19</a></i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">v</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="c1">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c3">w</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">v</font></span>)</span></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> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="csspace.html#D4" target="_self" title="CSSPACE:def.4">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c2">v</font></span>)</span></span>)</span></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> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="csspace.html#T5" target="_self" title="CSSPACE:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c2">v</font></span>)</span></span>)</span></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> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="csspace.html#T5" target="_self" title="CSSPACE:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c2">v</font></span>)</span></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> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="csspace.html#T3" target="_self" title="CSSPACE:th.3">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c2">v</font></span>)</span></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <font color="Maroon" title="c3">w</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="csspace.html#T3" target="_self" title="CSSPACE:th.3">Th3</a></i>
;<br/>
<b>hence </b><a NAME="E3:15"/>
<font color="Maroon" title="c1">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">w</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">v</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="c1">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c3">w</font></span>)</span>
 <b>by </b><i><a class="txt" href="csspace.html#E1:15"><i><font color="Green" title="E15">A1</font></i></a></i>;<br/>


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