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<b>consider </b><font color="Maroon">c<sub>1</sub></font> being  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">c<sub>2</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>3</sub></font> being   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>4</sub></font> being   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K2">COMPLEX</a> ,<font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,<font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:8_1_1"/><i><font color="Green">E3</font></i>: 
( ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="clvect_1.html#NM1">VECTOR</a> of <a href="clvect_1.html#G1" target="_self">CLSStruct</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> #) holds <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="clvect_1.html#NM1">VECTOR</a> of <a href="clvect_1.html#G1" target="_self">CLSStruct</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> #) holds <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>3</sub></font></span>)</span> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="clvect_1.html#NM1">VECTOR</a> of <a href="clvect_1.html#G1" target="_self">CLSStruct</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> #) holds <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <a href="clvect_1.html#G1" target="_self">CLSStruct</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> #)</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="clvect_1.html#NM1">VECTOR</a> of <a href="clvect_1.html#G1" target="_self">CLSStruct</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> #)ex <font color="Olive">b<sub>2</sub></font> being  <a href="clvect_1.html#NM1">VECTOR</a> of <a href="clvect_1.html#G1" target="_self">CLSStruct</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> #) st <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <a href="clvect_1.html#G1" target="_self">CLSStruct</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> #) ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="cfunct_1.html#NM1">Complex</a><br/>for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="clvect_1.html#NM1">VECTOR</a> of <a href="clvect_1.html#G1" target="_self">CLSStruct</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> #) holds <font color="Olive">b<sub>1</sub></font> <a href="clvect_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span> ) &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="cfunct_1.html#NM1">Complex</a><br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="clvect_1.html#NM1">VECTOR</a> of <a href="clvect_1.html#G1" target="_self">CLSStruct</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> #) holds <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="complex1.html#K8">+</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span> ) &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="cfunct_1.html#NM1">Complex</a><br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="clvect_1.html#NM1">VECTOR</a> of <a href="clvect_1.html#G1" target="_self">CLSStruct</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> #) holds <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="complex1.html#K9">*</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="clvect_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="clvect_1.html#K1" target="_self">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="clvect_1.html#NM1">VECTOR</a> of <a href="clvect_1.html#G1" target="_self">CLSStruct</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> #) holds <a href="complex1.html#K6">1r</a>  <a href="clvect_1.html#K1" target="_self">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>by </b><i><a class="txt" href="clvect_1.html#E2"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<b>take </b>
 <a href="clvect_1.html#G1" target="_self">CLSStruct</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> #)
;<br/>

<b>thus </b><a NAME="E3:8_1_1"/>
not  <a href="clvect_1.html#G1" target="_self">CLSStruct</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> #) is <a href="struct_0.html#V3">empty</a>
 ;<br/>

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


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