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<b>set </b><font color="Maroon" title="c3">nV</font> = <font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K7" title="PRVECT_1:func.7">-VectSp_over</a> <font color="Maroon" title="c1">K</font>;<br/>
<div><i><font color="Green" title="E101">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="119_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">u</font>, <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c6">w</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K7" title="PRVECT_1:func.7">-VectSp_over</a> <font color="Maroon" title="c1">K</font></span>)</span>;<br/><b>reconsider </b><font color="Maroon" title="c7">V</font> = <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c8">U</font> = <font color="Maroon" title="c4">u</font>, <font color="Maroon" title="c9">W</font> = <font color="Maroon" title="c6">w</font>, <font color="Maroon" title="c10">UV</font> = <font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c11">VW</font> = <font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c6">w</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">K</font> <b>by </b><i><a class="ref" href="matrix13.html#T102" target="_self" title="MATRIX13:th.102">TT102</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c6">w</font> = 
<font color="Maroon" title="c10">UV</font> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <font color="Maroon" title="c9">W</font>
<b>by </b><i><a class="ref" href="matrix13.html#T102" target="_self" title="MATRIX13:th.102">TT102</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">U</font> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <font color="Maroon" title="c7">V</font></span>)</span> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <font color="Maroon" title="c9">W</font>
<b>by </b><i><a class="ref" href="matrix13.html#T102" target="_self" title="MATRIX13:th.102">TT102</a></i>
<br/>.= 
<font color="Maroon" title="c8">U</font> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">V</font> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <font color="Maroon" title="c9">W</font></span>)</span>
<b>by </b><i><a class="ref" href="finseqop.html#T29" title="FINSEQOP:th.29">FINSEQOP:29</a></i>
<br/>.= 
<font color="Maroon" title="c8">U</font> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <font color="Maroon" title="c11">VW</font>
<b>by </b><i><a class="ref" href="matrix13.html#T102" target="_self" title="MATRIX13:th.102">TT102</a></i>
<br/>.= 
<font color="Maroon" title="c4">u</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c6">w</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix13.html#T102" target="_self" title="MATRIX13:th.102">TT102</a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E102">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="119_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">v</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K7" title="PRVECT_1:func.7">-VectSp_over</a> <font color="Maroon" title="c1">K</font></span>)</span>;<br/><b>reconsider </b><font color="Maroon" title="c5">V</font> = <font color="Maroon" title="c4">v</font>, <font color="Maroon" title="c6">n0</font> =  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K7" title="PRVECT_1:func.7">-VectSp_over</a> <font color="Maroon" title="c1">K</font></span>)</span> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">K</font> <b>by </b><i><a class="ref" href="matrix13.html#T102" target="_self" title="MATRIX13:th.102">TT102</a></i>;<br/><b>thus </b><font color="Maroon" title="c4">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K7" title="PRVECT_1:func.7">-VectSp_over</a> <font color="Maroon" title="c1">K</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c5">V</font> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <font color="Maroon" title="c6">n0</font>
<b>by </b><i><a class="ref" href="matrix13.html#T102" target="_self" title="MATRIX13:th.102">TT102</a></i>
<br/>.= 
<font color="Maroon" title="c5">V</font> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix13.html#T102" target="_self" title="MATRIX13:th.102">TT102</a></i>
<br/>.= 
<font color="Maroon" title="c4">v</font>
<b>by </b><i><a class="ref" href="fvsum_1.html#T28" title="FVSUM_1:th.28">FVSUM_1:28</a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E103">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="119_1_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">v</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K7" title="PRVECT_1:func.7">-VectSp_over</a> <font color="Maroon" title="c1">K</font></span>)</span>;<br/><b>reconsider </b><font color="Maroon" title="c5">V</font> = <font color="Maroon" title="c4">v</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">K</font> <b>by </b><i><a class="ref" href="matrix13.html#T102" target="_self" title="MATRIX13:th.102">TT102</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c6">u</font> =  <a href="fvsum_1.html#K6" title="FVSUM_1:func.6">-</a> <font color="Maroon" title="c5">V</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K7" title="PRVECT_1:func.7">-VectSp_over</a> <font color="Maroon" title="c1">K</font></span>)</span> <b>by </b><i><a class="ref" href="matrix13.html#T102" target="_self" title="MATRIX13:th.102">TT102</a></i>;<br/><font color="Maroon" title="c4">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c6">u</font> = 
<font color="Maroon" title="c5">V</font> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K6" title="FVSUM_1:func.6">-</a> <font color="Maroon" title="c5">V</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix13.html#T102" target="_self" title="MATRIX13:th.102">TT102</a></i>
<br/>.= 
<font color="Maroon" title="c2">n</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>
<b>by </b><i><a class="ref" href="fvsum_1.html#T35" title="FVSUM_1:th.35">FVSUM_1:35</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K7" title="PRVECT_1:func.7">-VectSp_over</a> <font color="Maroon" title="c1">K</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix13.html#T102" target="_self" title="MATRIX13:th.102">TT102</a></i>
;<br/><b>hence </b><a NAME="E4:119_1_1_3"/>
 ex <font color="Olive" title="b1">u</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K7" title="PRVECT_1:func.7">-VectSp_over</a> <font color="Maroon" title="c1">K</font></span>)</span> st <font color="Maroon" title="c4">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K7" title="PRVECT_1:func.7">-VectSp_over</a> <font color="Maroon" title="c1">K</font></span>)</span>
 ;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E104">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="119_1_1_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">v</font>, <font color="Maroon" title="c5">u</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K7" title="PRVECT_1:func.7">-VectSp_over</a> <font color="Maroon" title="c1">K</font></span>)</span>;<br/><b>reconsider </b><font color="Maroon" title="c6">V</font> = <font color="Maroon" title="c4">v</font>, <font color="Maroon" title="c7">U</font> = <font color="Maroon" title="c5">u</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">K</font> <b>by </b><i><a class="ref" href="matrix13.html#T102" target="_self" title="MATRIX13:th.102">TT102</a></i>;<br/><b>thus </b><font color="Maroon" title="c4">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c5">u</font> = 
<font color="Maroon" title="c6">V</font> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <font color="Maroon" title="c7">U</font>
<b>by </b><i><a class="ref" href="matrix13.html#T102" target="_self" title="MATRIX13:th.102">TT102</a></i>
<br/>.= 
<font color="Maroon" title="c7">U</font> <a href="fvsum_1.html#K4" title="FVSUM_1:func.4">+</a> <font color="Maroon" title="c6">V</font>
<b>by </b><i><a class="ref" href="finseqop.html#T34" title="FINSEQOP:th.34">FINSEQOP:34</a></i>
<br/>.= 
<font color="Maroon" title="c5">u</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c4">v</font>
<b>by </b><i><a class="ref" href="matrix13.html#T102" target="_self" title="MATRIX13:th.102">TT102</a></i>
;<br/></div><b>end;</b></div>
<b>thus </b><a NAME="E5:119_1_1"/>
<font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K7" title="PRVECT_1:func.7">-VectSp_over</a> <font color="Maroon" title="c1">K</font> is  <a href="vectsp_1.html#V11" title="VECTSP_1:attr.11">strict</a> <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font>
 <b>by </b><i><a class="txt" href="matrix13.html#E1:119_1_1"><i><font color="Green" title="E101">A1</font></i></a>, <a class="txt" href="matrix13.html#E2:119_1_1"><i><font color="Green" title="E102">A2</font></i></a>, <a class="txt" href="matrix13.html#E3:119_1_1"><i><font color="Green" title="E103">A3</font></i></a>, <a class="txt" href="matrix13.html#E4:119_1_1"><i><font color="Green" title="E104">A4</font></i></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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