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

<b>let </b><font color="Maroon" title="c1">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/><b>let </b><font color="Maroon" title="c2">W</font>, <font color="Maroon" title="c3">V</font> be   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">F</font>;<br/><b>let </b><font color="Maroon" title="c4">T</font> be   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c2">W</font>;<br/><b>let </b><font color="Maroon" title="c5">l</font> be    <a href="vectsp_6.html#M1" title="VECTSP_6:mode.1">Linear_Combination</a> of <font color="Maroon" title="c3">V</font>;<br/><b>let </b><font color="Maroon" title="c6">G</font> be   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c3">V</font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:52"/><i><font color="Green" title="E38">A1</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">G</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="c5">l</font>
 <b>and </b><br/><a NAME="E2:52"/><i><font color="Green" title="E39">A2</font></i>: 
<font color="Maroon" title="c4">T</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K1" title="VECTSP_6:func.1">Carrier</a> <font color="Maroon" title="c5">l</font></span>)</span> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c7">L</font> = <font color="Maroon" title="c4">T</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">G</font></span>)</span> as   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c2">W</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c8">R</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="ranknull.html#K8" title="RANKNULL:func.8">@</a> <font color="Maroon" title="c5">l</font></span>)</span> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">G</font></span>)</span> as   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c2">W</font> ;<br/>
<i><font color="Green" title="E40">A3</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">L</font> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">G</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_2.html#T37" title="FINSEQ_2:th.37">FINSEQ_2:37</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">G</font>
<b>by </b><i><a class="ref" href="vectsp_6.html#D8" title="VECTSP_6:def.8">VECTSP_6:def 8</a></i>
;<br/>
<i><font color="Green" title="E41">A4</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">R</font> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">G</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_6.html#D8" title="VECTSP_6:def.8">VECTSP_6:def 8</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">G</font>
<b>by </b><i><a class="ref" href="finseq_2.html#T37" title="FINSEQ_2:th.37">FINSEQ_2:37</a></i>
;<br/>
<a NAME="E7:52"/>
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> <font color="Maroon" title="c7">L</font> holds <br/><font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">R</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:52_3"/><i><font color="Green" title="E42">A5</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">k</font>
 <b>and </b><br/><a NAME="E2:52_3"/><i><font color="Green" title="E43">A6</font></i>: 
<font color="Maroon" title="c9">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> <font color="Maroon" title="c7">L</font>
 ;<br/>

<a NAME="E3:52_3"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">G</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">G</font>
 
<b>by </b><i><a class="ref" href="vectsp_6.html#D8" title="VECTSP_6:def.8">VECTSP_6:def 8</a></i>;<br/>
<a NAME="E4:52_3"/><b>then </b><i><font color="Green" title="E44">A7</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">G</font></span>)</span> <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> <font color="Maroon" title="c6">G</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E5:52_3"/>
<font color="Maroon" title="c9">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E6:52_3"/><b>then </b><i><font color="Green" title="E45">A8</font></i>: 
<font color="Maroon" title="c9">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">G</font></span>)</span>
 
<b>by </b><i><a class="txt" href="ranknull.html#E5:52"><i><font color="Green" title="E40">A3</font></i></a>, <a class="txt" href="ranknull.html#E1:52_3"><i><font color="Green" title="E42">A5</font></i></a>, <a class="txt" href="ranknull.html#E2:52_3"><i><font color="Green" title="E43">A6</font></i></a>, <a class="txt" href="ranknull.html#E4:52_3"><i><font color="Green" title="E44">A7</font></i></a></i>;<br/>
<a NAME="E7:52_3"/><b>then </b><i><font color="Green" title="E46">A9</font></i>: 
<font color="Maroon" title="c9">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">G</font>
 
<b>by </b><i><a class="txt" href="ranknull.html#E4:52_3"><i><font color="Green" title="E44">A7</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E8:52_3"/><b>then </b><i><font color="Green" title="E47">A10</font></i>: 
<font color="Maroon" title="c6">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">G</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">gk</font> = <font color="Maroon" title="c6">G</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">k</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">V</font> ;<br/>
<a NAME="E10:52_3"/><i><font color="Green" title="E48">A11</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">G</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> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">gk</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c10">gk</font>
 
<b>by </b><i><a class="txt" href="ranknull.html#E6:52_3"><i><font color="Green" title="E45">A8</font></i></a>, <a class="ref" href="vectsp_6.html#D8" title="VECTSP_6:def.8">VECTSP_6:def 8</a></i>;<br/>
<a NAME="E11:52_3"/><i><font color="Green" title="E49">A12</font></i>: 
<font color="Maroon" title="c6">G</font> <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="c6">G</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">k</font>
 
<b>by </b><i><a class="txt" href="ranknull.html#E7:52_3"><i><font color="Green" title="E46">A9</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c11">Gk</font> = <font color="Maroon" title="c6">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">V</font> ;<br/>
<a NAME="E13:52_3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">G</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">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">Gk</font>
 
<b>by </b><i><a class="txt" href="ranknull.html#E7:52_3"><i><font color="Green" title="E46">A9</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c12">TGk</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">W</font> ;<br/>
<i><font color="Green" title="E50">A13</font></i>: <font color="Maroon" title="c7">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font> = 
<font color="Maroon" title="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">gk</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c10">gk</font></span>)</span>
<b>by </b><i><a class="txt" href="ranknull.html#E6:52_3"><i><font color="Green" title="E45">A8</font></i></a>, <a class="txt" href="ranknull.html#E10:52_3"><i><font color="Green" title="E48">A11</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">gk</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="c4">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">gk</font></span>)</span>
<b>by </b><i><a class="ref" href="mod_2.html#D5" title="MOD_2:def.5">MOD_2:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">Gk</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c12">TGk</font>
<b>by </b><i><a class="txt" href="ranknull.html#E7:52_3"><i><font color="Green" title="E46">A9</font></i></a>, <a class="txt" href="ranknull.html#E11:52_3"><i><font color="Green" title="E49">A12</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
;<br/>
<a NAME="E16:52_3"/><i><font color="Green" title="E51">A14</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c8">R</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> <font color="Maroon" title="c6">G</font></span>)</span>
 
<b>by </b><i><a class="txt" href="ranknull.html#E6:52"><i><font color="Green" title="E41">A4</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E17:52_3"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c3">V</font>
 
<b>by </b><i><a class="ref" href="ranknull.html#T7" target="_self" title="RANKNULL:th.7">Th7</a></i>;<br/>
<a NAME="E18:52_3"/><b>then </b>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">G</font>
 
<b>by </b><i><a class="txt" href="ranknull.html#E1:52"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="relat_1.html#T46" title="RELAT_1:th.46">RELAT_1:46</a></i>;<br/>
<a NAME="E19:52_3"/><b>then </b><i><font color="Green" title="E52">A15</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">G</font></span>)</span> <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> <span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font>
 
<b>by </b><i><a class="txt" href="ranknull.html#E7:52_3"><i><font color="Green" title="E46">A9</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>;<br/>
<a NAME="E20:52_3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="ranknull.html#K8" title="RANKNULL:func.8">@</a> <font color="Maroon" title="c5">l</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_3_2"><b>proof </b></a><div class="add">

<a NAME="E1:52_3_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">G</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">T</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font></span>)</span>
 
<b>by </b><i><a class="txt" href="ranknull.html#E7:52_3"><i><font color="Green" title="E46">A9</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>;<br/>
<b>hence </b><a NAME="E2:52_3_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="ranknull.html#K8" title="RANKNULL:func.8">@</a> <font color="Maroon" title="c5">l</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="ranknull.html#E1:52"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="ranknull.html#E2:52"><i><font color="Green" title="E39">A2</font></i></a>, <a class="txt" href="ranknull.html#E8:52_3"><i><font color="Green" title="E47">A10</font></i></a>, <a class="ref" href="ranknull.html#T37" target="_self" title="RANKNULL:th.37">Th37</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E21:52_3"/>
<font color="Maroon" title="c7">L</font> <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="c8">R</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font>
 <b>by </b><i><a class="txt" href="ranknull.html#E4:52_3"><i><font color="Green" title="E44">A7</font></i></a>, <a class="txt" href="ranknull.html#E6:52_3"><i><font color="Green" title="E45">A8</font></i></a>, <a class="txt" href="ranknull.html#E15:52_3"><i><font color="Green" title="E50">A13</font></i></a>, <a class="txt" href="ranknull.html#E16:52_3"><i><font color="Green" title="E51">A14</font></i></a>, <a class="txt" href="ranknull.html#E19:52_3"><i><font color="Green" title="E52">A15</font></i></a>, <a class="ref" href="vectsp_6.html#D8" title="VECTSP_6:def.8">VECTSP_6:def 8</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E8:52"/>
<font color="Maroon" title="c4">T</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <font color="Maroon" title="c6">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="ranknull.html#K8" title="RANKNULL:func.8">@</a> <font color="Maroon" title="c5">l</font></span>)</span> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">T</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="ranknull.html#E5:52"><i><font color="Green" title="E40">A3</font></i></a>, <a class="txt" href="ranknull.html#E6:52"><i><font color="Green" title="E41">A4</font></i></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</a></i>;<br/>


</div>
