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<span class="kw">let </span><font color="Maroon" title="c2">C</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="clvect_1.html#V1" title="CLVECT_1:attr.1">strict</a>   <a href="clvect_1.html#L1" title="CLVECT_1:struct.1">CLSStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cfuncdom.html#K6" title="CFUNCDOM:func.6">ComplexVectSpace</a> <font color="Maroon" title="c1">A</font> implies ( <font color="Maroon" title="c2">C</font> is  <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V2" title="CLVECT_1:attr.2">vector-distributive</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V3" title="CLVECT_1:attr.3">scalar-distributive</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V4" title="CLVECT_1:attr.4">scalar-associative</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">scalar-unital</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:31_1_1"/><span class="lab"><font color="Green" title="E25">Z</font></span>: 
<font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cfuncdom.html#K6" title="CFUNCDOM:func.6">ComplexVectSpace</a> <font color="Maroon" title="c1">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">C</font> is  <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V2" title="CLVECT_1:attr.2">vector-distributive</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V3" title="CLVECT_1:attr.3">scalar-distributive</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V4" title="CLVECT_1:attr.4">scalar-associative</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">scalar-unital</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E2:31_1_1"/>
 for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">C</font> holds  <font color="Olive" title="b1">u</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b1">u</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cfuncdom.html#T5" target="_self" title="CFUNCDOM:th.5">Th7</a>, <a class="txt" href="#E1:31_1_1"><span class="lab"><font color="Green" title="E25">Z</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="rlvect_1.html#D2" title="RLVECT_1:def.2">RLVECT_1:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">C</font> is  <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V2" title="CLVECT_1:attr.2">vector-distributive</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V3" title="CLVECT_1:attr.3">scalar-distributive</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V4" title="CLVECT_1:attr.4">scalar-associative</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">scalar-unital</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E3:31_1_1"/>
 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="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">C</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</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="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">w</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cfuncdom.html#T6" target="_self" title="CFUNCDOM:th.6">Th8</a>, <a class="txt" href="#E1:31_1_1"><span class="lab"><font color="Green" title="E25">Z</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="rlvect_1.html#D3" title="RLVECT_1:def.3">RLVECT_1:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">C</font> is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V2" title="CLVECT_1:attr.2">vector-distributive</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V3" title="CLVECT_1:attr.3">scalar-distributive</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V4" title="CLVECT_1:attr.4">scalar-associative</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">scalar-unital</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E4:31_1_1"/>
 for <font color="Olive" title="b1">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">C</font> holds  <font color="Olive" title="b1">u</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">u</font>
  <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="rlvect_1.html#D4" title="RLVECT_1:def.4">RLVECT_1:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">C</font> is  <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V2" title="CLVECT_1:attr.2">vector-distributive</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V3" title="CLVECT_1:attr.3">scalar-distributive</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V4" title="CLVECT_1:attr.4">scalar-associative</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">scalar-unital</a>  )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">u</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">u</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c4">v</font> = <font color="Maroon" title="c3">u</font> as    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c1">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>) <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31_1_1"><span class="lab"><font color="Green" title="E25">Z</font></span></a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c3">u</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">C</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="cfuncdom.html#K1" title="CFUNCDOM:func.1">ComplexFuncAdd</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> (<span class="p1">(<span class="default"><a href="cfuncdom.html#K4" title="CFUNCDOM:func.4">ComplexFuncZero</a> <font color="Maroon" title="c1">A</font></span>)</span>,<font color="Maroon" title="c4">v</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="cfuncdom.html#T5" target="_self" title="CFUNCDOM:th.5">Th7</a>, <a class="txt" href="#E1:31_1_1"><span class="lab"><font color="Green" title="E25">Z</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c3">u</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cfuncdom.html#T10" target="_self" title="CFUNCDOM:th.10">Th12</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E5:31_1_1"/>
 for <font color="Olive" title="b1">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">C</font> holds  <font color="Olive" title="b1">u</font> is  <a href="algstr_0.html#V10" title="ALGSTR_0:attr.10">right_complementable</a> 
  <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="algstr_0.html#D16" title="ALGSTR_0:def.16">ALGSTR_0:def 16</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V2" title="CLVECT_1:attr.2">vector-distributive</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V3" title="CLVECT_1:attr.3">scalar-distributive</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V4" title="CLVECT_1:attr.4">scalar-associative</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">scalar-unital</a>  )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">u</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">u</font> is  <a href="algstr_0.html#V10" title="ALGSTR_0:attr.10">right_complementable</a> </span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c4">v</font> = <font color="Maroon" title="c3">u</font> as    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c1">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>) <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31_1_1"><span class="lab"><font color="Green" title="E25">Z</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">w</font> = <span class="p1">(<span class="default"><a href="cfuncdom.html#K3" title="CFUNCDOM:func.3">ComplexFuncExtMult</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcsdom.html#K2" title="FUNCSDOM:func.2">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a></span>)</span>,<font color="Maroon" title="c4">v</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c2">C</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31_1_1"><span class="lab"><font color="Green" title="E25">Z</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c5">w</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="algstr_0.html#D11" title="ALGSTR_0:def.11">ALGSTR_0:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="c5">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">C</font></span><br/>

<span class="kw">thus </span><a NAME="E3:31_1_1_2"/>
<font color="Maroon" title="c3">u</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cfuncdom.html#T11" target="_self" title="CFUNCDOM:th.11">Th13</a>, <a class="txt" href="#E1:31_1_1"><span class="lab"><font color="Green" title="E25">Z</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E6:31_1_1"/>
 for <font color="Olive" title="b1">a</font> being   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a><br/>  for <font color="Olive" title="b2">u</font>, <font color="Olive" title="b3">v</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">C</font> holds  <font color="Olive" title="b1">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">u</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b2">u</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b3">v</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="cfuncdom.html#E21"><span class="lab"><font color="Green" title="E18">Lm2</font></span></a>, <a class="txt" href="#E1:31_1_1"><span class="lab"><font color="Green" title="E25">Z</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="clvect_1.html#D2" title="CLVECT_1:def.2">CLVECT_1:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V3" title="CLVECT_1:attr.3">scalar-distributive</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V4" title="CLVECT_1:attr.4">scalar-associative</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">scalar-unital</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E7:31_1_1"/>
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</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="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">C</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <font color="Olive" title="b2">b</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">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b3">v</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b3">v</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cfuncdom.html#T14" target="_self" title="CFUNCDOM:th.14">Th16</a>, <a class="txt" href="#E1:31_1_1"><span class="lab"><font color="Green" title="E25">Z</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="clvect_1.html#D3" title="CLVECT_1:def.3">CLVECT_1:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V4" title="CLVECT_1:attr.4">scalar-associative</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">scalar-unital</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E8:31_1_1"/>
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</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="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">C</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Olive" title="b2">b</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">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b3">v</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cfuncdom.html#T13" target="_self" title="CFUNCDOM:th.13">Th15</a>, <a class="txt" href="#E1:31_1_1"><span class="lab"><font color="Green" title="E25">Z</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="clvect_1.html#D4" title="CLVECT_1:def.4">CLVECT_1:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">C</font> is  <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">scalar-unital</a> </span><br/>

<span class="kw">thus </span><a NAME="E9:31_1_1"/>
 for <font color="Olive" title="b1">v</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">C</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cfuncdom.html#T12" target="_self" title="CFUNCDOM:th.12">Th14</a>, <a class="txt" href="#E1:31_1_1"><span class="lab"><font color="Green" title="E25">Z</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="clvect_1.html#D5" title="CLVECT_1:def.5">CLVECT_1:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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