<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c4">l</font> be    <a href="csspace.html#L1" title="CSSPACE:struct.1">CUNITSTR</a> ;<br/>

<b>assume </b><a NAME="E1:115"/><i><font color="Green" title="E73">A1</font></i>: 
 <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">l</font>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">Zero</a> of <font color="Maroon" title="c4">l</font>,the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c4">l</font>,the <a href="clvect_1.html#U1" title="CLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c4">l</font> #) is   <a href="clvect_1.html#NM2" title="CLVECT_1:NM.2">ComplexLinearSpace</a>
 ;<br/>

<a NAME="E2:115"/>
not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">l</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="txt" href="csspace.html#E1:115"><i><font color="Green" title="E73">A1</font></i></a>, <a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">l</font> = <font color="Maroon" title="c4">l</font> as  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="clvect_1.html#L1" title="CLVECT_1:struct.1">CLSStruct</a>  <b>by </b><i><a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">l0</font> =  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">l</font>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">Zero</a> of <font color="Maroon" title="c5">l</font>,the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c5">l</font>,the <a href="clvect_1.html#U1" title="CLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c5">l</font> #) as   <a href="clvect_1.html#NM2" title="CLVECT_1:NM.2">ComplexLinearSpace</a> <b>by </b><i><a class="txt" href="csspace.html#E1:115"><i><font color="Green" title="E73">A1</font></i></a></i>;<br/>
<a NAME="E5:115"/><i><font color="Green" title="E74">A2</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 <font color="Maroon" title="c5">l</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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="115_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">v</font>, <font color="Maroon" title="c8">w</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c5">l</font>;<br/>

<b>reconsider </b><font color="Maroon" title="c9">v1</font> = <font color="Maroon" title="c7">v</font> as   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c6">l0</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c10">w1</font> = <font color="Maroon" title="c8">w</font> as   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c6">l0</font> ;<br/>
<b>thus </b><font color="Maroon" title="c7">v</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Maroon" title="c8">w</font> = 
<font color="Maroon" title="c9">v1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c10">w1</font>

<br/>.= 
<font color="Maroon" title="c8">w</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Maroon" title="c7">v</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#D3" title="RLVECT_1:def.3">RLVECT_1:def 3</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E6:115"/><i><font color="Green" title="E75">A3</font></i>: 
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 <font color="Maroon" title="c5">l</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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="115_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">u</font>, <font color="Maroon" title="c8">v</font>, <font color="Maroon" title="c9">w</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c5">l</font>;<br/>

<b>reconsider </b><font color="Maroon" title="c10">u1</font> = <font color="Maroon" title="c7">u</font> as   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c6">l0</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c11">v1</font> = <font color="Maroon" title="c8">v</font> as   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c6">l0</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c12">w1</font> = <font color="Maroon" title="c9">w</font> as   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c6">l0</font> ;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c7">u</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Maroon" title="c8">v</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Maroon" title="c9">w</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c11">v1</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c12">w1</font>

<br/>.= 
<font color="Maroon" title="c10">u1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">v1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c12">w1</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c7">u</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Maroon" title="c9">w</font></span>)</span>

;<br/>


</div><b>end;</b></div>
<a NAME="E7:115"/><i><font color="Green" title="E76">A4</font></i>: 
for <font color="Olive" title="b1">v</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c5">l</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> <font color="Maroon" title="c5">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="115_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">v</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c5">l</font>;<br/>

<b>reconsider </b><font color="Maroon" title="c8">v1</font> = <font color="Maroon" title="c7">v</font> as   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c6">l0</font> ;<br/>
<b>thus </b><font color="Maroon" title="c7">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> <font color="Maroon" title="c5">l</font></span>)</span> = 
<font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c6">l0</font></span>)</span>

<br/>.= 
<font color="Maroon" title="c7">v</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E8:115"/><i><font color="Green" title="E77">A5</font></i>: 
for <font color="Olive" title="b1">v</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c5">l</font>  ex <font color="Olive" title="b2">w</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c5">l</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> <font color="Maroon" title="c5">l</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="115_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">v</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c5">l</font>;<br/>

<b>reconsider </b><font color="Maroon" title="c8">v1</font> = <font color="Maroon" title="c7">v</font> as   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c6">l0</font> ;<br/>
<b>consider </b><font color="Maroon" title="c9">w1</font> being   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c6">l0</font><b> such that </b><br/><a NAME="E3:115_4"/><i><font color="Green" title="E78">A6</font></i>: 
<font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c9">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c6">l0</font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D8" title="RLVECT_1:def.8">RLVECT_1:def 8</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">w</font> = <font color="Maroon" title="c9">w1</font> as   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c5">l</font> ;<br/>
<a NAME="E5:115_4"/><i><font color="Green" title="E79">A7</font></i>: 
<font color="Maroon" title="c7">v</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Maroon" title="c10">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> <font color="Maroon" title="c5">l</font>
 
<b>by </b><i><a class="txt" href="csspace.html#E3:115_4"><i><font color="Green" title="E78">A6</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c10">w</font>
;<br/>

<b>thus </b><a NAME="E6:115_4"/>
<font color="Maroon" title="c7">v</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Maroon" title="c10">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> <font color="Maroon" title="c5">l</font>
 <b>by </b><i><a class="txt" href="csspace.html#E5:115_4"><i><font color="Green" title="E79">A7</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:115"/><i><font color="Green" title="E78">A8</font></i>: 
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 <font color="Maroon" title="c5">l</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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="115_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">z</font> be   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a>;<br/><b>let </b><font color="Maroon" title="c8">v</font>, <font color="Maroon" title="c9">w</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c5">l</font>;<br/>



<b>reconsider </b><font color="Maroon" title="c10">v1</font> = <font color="Maroon" title="c8">v</font>, <font color="Maroon" title="c11">w1</font> = <font color="Maroon" title="c9">w</font> as   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c6">l0</font> ;<br/>
<b>thus </b><font color="Maroon" title="c7">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Maroon" title="c9">w</font></span>)</span> = 
<font color="Maroon" title="c7">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">v1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c11">w1</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c10">v1</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c11">w1</font></span>)</span>
<b>by </b><i><a class="ref" href="clvect_1.html#D2" title="CLVECT_1:def.2">CLVECT_1:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c8">v</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c9">w</font></span>)</span>

;<br/>


</div><b>end;</b></div>
<a NAME="E10:115"/><i><font color="Green" title="E79">A9</font></i>: 
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 <font color="Maroon" title="c5">l</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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="115_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">z1</font>, <font color="Maroon" title="c8">z2</font> be   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a>;<br/><b>let </b><font color="Maroon" title="c9">v</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c5">l</font>;<br/>



<b>reconsider </b><font color="Maroon" title="c10">v1</font> = <font color="Maroon" title="c9">v</font> as   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c6">l0</font> ;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c7">z1</font> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <font color="Maroon" title="c8">z2</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c9">v</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">z1</font> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <font color="Maroon" title="c8">z2</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c10">v1</font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">z1</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c10">v1</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">z2</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c10">v1</font></span>)</span>
<b>by </b><i><a class="ref" href="clvect_1.html#D2" title="CLVECT_1:def.2">CLVECT_1:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">z1</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c9">v</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">z2</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c9">v</font></span>)</span>

;<br/>


</div><b>end;</b></div>
<a NAME="E11:115"/><i><font color="Green" title="E80">A10</font></i>: 
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 <font color="Maroon" title="c5">l</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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="115_7"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">z1</font>, <font color="Maroon" title="c8">z2</font> be   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a>;<br/><b>let </b><font color="Maroon" title="c9">v</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c5">l</font>;<br/>



<b>reconsider </b><font color="Maroon" title="c10">v1</font> = <font color="Maroon" title="c9">v</font> as   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c6">l0</font> ;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c7">z1</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c8">z2</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c9">v</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">z1</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c8">z2</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c10">v1</font>

<br/>.= 
<font color="Maroon" title="c7">z1</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">z2</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c10">v1</font></span>)</span>
<b>by </b><i><a class="ref" href="clvect_1.html#D2" title="CLVECT_1:def.2">CLVECT_1:def 2</a></i>
<br/>.= 
<font color="Maroon" title="c7">z1</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">z2</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c9">v</font></span>)</span>

;<br/>


</div><b>end;</b></div>
<a NAME="E12:115"/>
for <font color="Olive" title="b1">v</font> being  <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c5">l</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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="115_8"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">v</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c5">l</font>;<br/>

<b>reconsider </b><font color="Maroon" title="c8">v1</font> = <font color="Maroon" title="c7">v</font> as   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c6">l0</font> ;<br/>
<b>thus </b><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="Maroon" title="c7">v</font> = 
<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="Maroon" title="c8">v1</font>

<br/>.= 
<font color="Maroon" title="c7">v</font>
<b>by </b><i><a class="ref" href="clvect_1.html#D2" title="CLVECT_1:def.2">CLVECT_1:def 2</a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E13:115"/>
<font color="Maroon" title="c4">l</font> is   <a href="clvect_1.html#NM2" title="CLVECT_1:NM.2">ComplexLinearSpace</a>
 <b>by </b><i><a class="txt" href="csspace.html#E5:115"><i><font color="Green" title="E74">A2</font></i></a>, <a class="txt" href="csspace.html#E6:115"><i><font color="Green" title="E75">A3</font></i></a>, <a class="txt" href="csspace.html#E7:115"><i><font color="Green" title="E76">A4</font></i></a>, <a class="txt" href="csspace.html#E8:115"><i><font color="Green" title="E77">A5</font></i></a>, <a class="txt" href="csspace.html#E9:115"><i><font color="Green" title="E78">A8</font></i></a>, <a class="txt" href="csspace.html#E10:115"><i><font color="Green" title="E79">A9</font></i></a>, <a class="txt" href="csspace.html#E11:115"><i><font color="Green" title="E80">A10</font></i></a>, <a class="ref" href="clvect_1.html#T1" title="CLVECT_1:th.1">CLVECT_1:1</a></i>;<br/>


</div>
