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<b>consider </b><font color="Maroon" title="c1">ZS</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> , <font color="Maroon" title="c2">O</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">ZS</font>, <font color="Maroon" title="c3">F</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c1">ZS</font>, <font color="Maroon" title="c4">G</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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> ,<font color="Maroon" title="c1">ZS</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Maroon" title="c1">ZS</font><b> such that </b><br/><a NAME="E2:8_1_1"/><i><font color="Green" title="E3">A1</font></i>: 
( ( for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</font> being  <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>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #) holds  <font color="Olive" title="b1">v</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Olive" title="b2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">w</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Olive" title="b1">v</font> ) &amp; ( for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</font> being  <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>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #) holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Olive" title="b3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">u</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Olive" title="b3">w</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">v</font> being  <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>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #) holds  <font color="Olive" title="b1">v</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v</font> ) &amp; ( for <font color="Olive" title="b1">v</font> being  <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>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #)  ex <font color="Olive" title="b2">w</font> being  <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>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #) st <font color="Olive" title="b1">v</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Olive" title="b2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #) ) &amp; ( for <font color="Olive" title="b1">z</font> being  <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a><br/> for <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</font> being  <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>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #) holds  <font color="Olive" title="b1">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Olive" title="b3">w</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b3">w</font></span>)</span> ) &amp; ( 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><br/> for <font color="Olive" title="b3">v</font> being  <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>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #) holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">z1</font> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <font color="Olive" title="b2">z2</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">z1</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b3">v</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">z2</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b3">v</font></span>)</span> ) &amp; ( 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><br/> for <font color="Olive" title="b3">v</font> being  <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>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #) holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">z1</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Olive" title="b2">z2</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">z1</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">z2</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b3">v</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">v</font> being  <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>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #) holds  <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a>  <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v</font> ) )
 <b>by </b><i><a class="txt" href="clvect_1.html#E2"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<b>take </b>
 <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #)
;<br/>

<b>thus </b><a NAME="E3:8_1_1"/>
not  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #) is <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>
 ;<br/>

<b>thus </b><a NAME="E4:8_1_1"/>
(  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #) is <a href="clvect_1.html#V1" title="CLVECT_1:attr.1">strict</a> &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #) is <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">Abelian</a> &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #) is <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #) is <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #) is <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a> &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c1">ZS</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">G</font> #) is <a href="clvect_1.html#V2" title="CLVECT_1:attr.2">ComplexLinearSpace-like</a> )
 <b>by </b><i><a class="txt" href="clvect_1.html#E2:8_1_1"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="clvect_1.html#D2" target="_self" title="CLVECT_1:def.2">Def2</a>, <a class="ref" href="rlvect_1.html#D5" title="RLVECT_1:def.5">RLVECT_1:def 5</a>, <a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a>, <a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a>, <a class="ref" href="rlvect_1.html#D8" title="RLVECT_1:def.8">RLVECT_1:def 8</a></i>;<br/>


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