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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V</font> being   <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">R</font><br/>  for <font color="Olive" title="b2">L</font> being    <a href="vectsp_6.html#M1" title="VECTSP_6:mode.1">Linear_Combination</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b3">a</font> being   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R</font> holds   <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Olive" title="b2">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <font color="Olive" title="b2">L</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">L</font> being    <a href="vectsp_6.html#M1" title="VECTSP_6:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font><br/>  for <font color="Olive" title="b2">a</font> being   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R</font> holds   <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Olive" title="b1">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <font color="Olive" title="b1">L</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">L</font> be    <a href="vectsp_6.html#M1" title="VECTSP_6:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R</font> holds   <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <font color="Maroon" title="c3">L</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">a</font> be   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <font color="Maroon" title="c3">L</font></span>)</span></span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">l</font> = <font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font>;<br/>
<a NAME="E1:4"/>
 <a href="vectsp_6.html#K1" title="VECTSP_6:func.1">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="vectsp_6.html#K1" title="VECTSP_6:func.1">Carrier</a> <font color="Maroon" title="c3">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_6.html#T28" title="VECTSP_6:th.28">VECTSP_6:28</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">F</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</font><span class="kw"> such that </span><br/><a NAME="E3:4"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
( <font color="Maroon" title="c6">F</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_6.html#K1" title="VECTSP_6:func.1">Carrier</a> <font color="Maroon" title="c3">L</font> )
 <span class="kw">and </span><br/><a NAME="E4:4"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
 <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mod_3.html#T2" target="_self" title="MOD_3:th.2">Th6</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">f</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">g</font> = <font color="Maroon" title="c3">L</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font>;<br/>
<span class="lab"><font color="Green" title="E7">A3</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">F</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_6.html#D5" title="VECTSP_6:def.5">VECTSP_6:def 5</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_6.html#D5" title="VECTSP_6:def.5">VECTSP_6:def 5</a></span>
;<br/>
<a NAME="E6:4"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_6.html#D5" title="VECTSP_6:def.5">VECTSP_6:def 5</a></span>;<br/>
<a NAME="E7:4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E8">A4</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E9">A5</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="4_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">v</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font>  st <font color="Maroon" title="c9">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font></span>)</span> &amp; <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Olive" title="b1">v</font></span><br/><span class="kw">let </span><font color="Maroon" title="c10">v</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</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="c9">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font></span>)</span> &amp; <font color="Maroon" title="c10">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c10">v</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:4_2"/><span class="lab"><font color="Green" title="E10">A6</font></span>: 
<font color="Maroon" title="c9">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:4_2"/><span class="lab"><font color="Green" title="E11">A7</font></span>: 
<font color="Maroon" title="c10">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c10">v</font></span><br/><span class="kw">set </span><font color="Maroon" title="c11">v9</font> = <font color="Maroon" title="c6">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">k</font>;<br/><a NAME="E3:4_2"/><span class="lab"><font color="Green" title="E12">A8</font></span>: 
<font color="Maroon" title="c9">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:4_2"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/><a NAME="E4:4_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A9</font></span>: 
<font color="Maroon" title="c6">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:4"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">k</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:4"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E3:4_2"><span class="lab"><font color="Green" title="E12">A8</font></span></a>, <a class="ref" href="vectsp_6.html#T8" title="VECTSP_6:th.8">VECTSP_6:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">k</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_6.html#D9" title="VECTSP_6:def.9">VECTSP_6:def 9</a></span>
<br/>.= 
<font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D16" title="VECTSP_1:def.16">VECTSP_1:def 16</a></span>
<br/>.= 
<font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c10">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:4"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E2:4_2"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="txt" href="#E3:4_2"><span class="lab"><font color="Green" title="E12">A8</font></span></a>, <a class="txt" href="#E4:4_2"><span class="lab"><font color="Green" title="E13">A9</font></span></a>, <a class="ref" href="vectsp_6.html#T8" title="VECTSP_6:th.8">VECTSP_6:8</a></span>
;<br/> <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>
<a NAME="E9:4"/>
 <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <font color="Maroon" title="c3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">F</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:4"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="vectsp_6.html#D6" title="VECTSP_6:def.6">VECTSP_6:def 6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:4"/>
 <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <font color="Maroon" title="c3">L</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:4"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E5:4"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E8:4"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="ref" href="rlvect_2.html#T66" title="RLVECT_2:th.66">RLVECT_2:66</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/>


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