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

<span class="kw">let </span><font color="Maroon" title="c1">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">V1</font> being  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font><br/> for <font color="Olive" title="b2">b1</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b1">V1</font><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="Olive" title="b1">V1</font> holds  <font color="Olive" title="b3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Olive" title="b2">b1</font></span>)</span>,<font color="Olive" title="b2">b1</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V1</font> be   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">b1</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c2">V1</font><br/> for <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">V1</font> holds  <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Olive" title="b1">b1</font></span>)</span>,<font color="Olive" title="b1">b1</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">b1</font> be    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c2">V1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> 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">V1</font> holds  <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span>,<font color="Maroon" title="c3">b1</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">v</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">V1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span>,<font color="Maroon" title="c3">b1</font></span>)</span></span><br/>







<span class="kw">consider </span><font color="Maroon" title="c5">KL</font> being    <a href="vectsp_6.html#M1" title="VECTSP_6:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V1</font><span class="kw"> such that </span><br/><a NAME="E2:54"/><span class="lab"><font color="Green" title="E41">A1</font></span>: 
( <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <font color="Maroon" title="c5">KL</font> &amp;  <a href="vectsp_6.html#K1" title="VECTSP_6:func.1">Carrier</a> <font color="Maroon" title="c5">KL</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">b1</font> )
 <span class="kw">and </span><br/><a NAME="E3:54"/><span class="lab"><font color="Green" title="E42">A2</font></span>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">KL</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D9" target="_self" title="MATRLIN:def.9">Def9</a></span>;<br/>
<a NAME="E4:54"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</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="c3">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D9" target="_self" title="MATRLIN:def.9">Def9</a></span>;<br/>
<a NAME="E5:54"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A3</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></span>;<br/>
<a NAME="E6:54"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A4</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span>,<font color="Maroon" title="c3">b1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#T16" target="_self" title="MATRLIN:th.16">Th16</a></span>;<br/>
<span class="lab"><font color="Green" title="E45">A5</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">KL</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c3">b1</font></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">b1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_6.html#D8" title="VECTSP_6:def.8">VECTSP_6:def 8</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span>,<font color="Maroon" title="c3">b1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:54"><span class="lab"><font color="Green" title="E44">A4</font></span></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></span>
;<br/>
<div><span class="lab"><font color="Green" title="E46">A6</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="54_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">t</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">t</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"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span>,<font color="Maroon" title="c3">b1</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c5">KL</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span>,<font color="Maroon" title="c3">b1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">t</font> )</span><br/><span class="kw">assume </span><a NAME="E1:54_2"/><span class="lab"><font color="Green" title="E47">A7</font></span>: 
<font color="Maroon" title="c6">t</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"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span>,<font color="Maroon" title="c3">b1</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c5">KL</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span>,<font color="Maroon" title="c3">b1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">t</font></span><br/><a NAME="E2:54_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A8</font></span>: 
<font color="Maroon" title="c3">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:54"><span class="lab"><font color="Green" title="E44">A4</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>;<br/><a NAME="E3:54_2"/>
<font color="Maroon" title="c6">t</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"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:54"><span class="lab"><font color="Green" title="E43">A3</font></span></a>, <a class="txt" href="#E1:54_2"><span class="lab"><font color="Green" title="E47">A7</font></span></a>, <a class="ref" href="matrlin.html#T16" target="_self" title="MATRLIN:th.16">Th16</a></span>;<br/><a NAME="E4:54_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A9</font></span>: 
<font color="Maroon" title="c6">t</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/><a NAME="E5:54_2"/><span class="lab"><font color="Green" title="E50">A10</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_2"><span class="lab"><font color="Green" title="E47">A7</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/><a NAME="E6:54_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A11</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:54_2"><span class="lab"><font color="Green" title="E49">A9</font></span></a>, <a class="ref" href="finseq_4.html#T24" title="FINSEQ_4:th.24">FINSEQ_4:24</a></span>;<br/><a NAME="E7:54_2"/>
<font color="Maroon" title="c6">t</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"><font color="Maroon" title="c5">KL</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c3">b1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:54"><span class="lab"><font color="Green" title="E45">A5</font></span></a>, <a class="txt" href="#E1:54_2"><span class="lab"><font color="Green" title="E47">A7</font></span></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><font color="Maroon" title="c5">KL</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">t</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">KL</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">t</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="c3">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">t</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_6.html#D8" title="VECTSP_6:def.8">VECTSP_6:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">t</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">t</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:54"><span class="lab"><font color="Green" title="E42">A2</font></span></a>, <a class="txt" href="#E5:54_2"><span class="lab"><font color="Green" title="E50">A10</font></span></a>, <a class="txt" href="#E4:54_2"><span class="lab"><font color="Green" title="E49">A9</font></span></a></span>
<br/>.= 
the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">lmult</a> of <font color="Maroon" title="c2">V1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">t</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">b1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">t</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:54_2"><span class="lab"><font color="Green" title="E48">A8</font></span></a>, <a class="txt" href="#E6:54_2"><span class="lab"><font color="Green" title="E51">A11</font></span></a>, <a class="ref" href="vectsp_1.html#D24" title="VECTSP_1:def.24">VECTSP_1:def 24</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span>,<font color="Maroon" title="c3">b1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">t</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_2"><span class="lab"><font color="Green" title="E47">A7</font></span></a>, <a class="ref" href="funcop_1.html#T28" title="FUNCOP_1:th.28">FUNCOP_1:28</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E9:54"/>
<font color="Maroon" title="c3">b1</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D4" target="_self" title="MATRLIN:def.4">Def4</a></span>;<br/>
<span class="kw">hence </span><font color="Maroon" title="c4">v</font> = 
 <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">KL</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c3">b1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:54"><span class="lab"><font color="Green" title="E41">A1</font></span></a>, <a class="ref" href="matrlin.html#T24" target="_self" title="MATRLIN:th.24">Th24</a></span>
<br/>.= 
 <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c3">b1</font></span>)</span>,<font color="Maroon" title="c3">b1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:54"><span class="lab"><font color="Green" title="E45">A5</font></span></a>, <a class="txt" href="#E8:54"><span class="lab"><font color="Green" title="E46">A6</font></span></a>, <a class="ref" href="newton.html#T3" title="NEWTON:th.3">NEWTON:3</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
