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<div class="add">

<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="vectsp_2.html#NM2" title="VECTSP_2:NM.2">domRing</a>;<br/><b>let </b><font color="Maroon" title="c2">V</font> be   <a href="vectsp_2.html#NM7" title="VECTSP_2:NM.7">RightMod</a> of <font color="Maroon" title="c1">R</font>;<br/><b>let </b><font color="Maroon" title="c3">L</font> be    <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font>;<br/><b>let </b><font color="Maroon" title="c4">a</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Scalar</a> of <font color="Maroon" title="c1">R</font>;<br/>







<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_1"/>
( <font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font> or <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1"><b>suppose </b></a><a NAME="E1:70_1_1"/><i><font color="Green" title="E41">A1</font></i>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font>
 ;<br/><div class="add"><b>consider </b><font color="Maroon" title="c5">F</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c2">V</font><b> such that </b><br/><a NAME="E3:70_1_1"/><i><font color="Green" title="E42">A2</font></i>: 
<font color="Maroon" title="c5">F</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>and </b><br/><a NAME="E4:70_1_1"/><i><font color="Green" title="E43">A3</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span>
 <b>and </b><br/><a NAME="E5:70_1_1"/><i><font color="Green" title="E44">A4</font></i>: 
 <a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K9" title="RLVECT_1:func.9">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c5">F</font></span>)</span>
 <b>by </b><i><a class="ref" href="rmod_4.html#D9" target="_self" title="RMOD_4:def.9">Def9</a></i>;<br/><b>consider </b><font color="Maroon" title="c6">G</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c2">V</font><b> such that </b><br/><a NAME="E7:70_1_1"/><i><font color="Green" title="E45">A5</font></i>: 
<font color="Maroon" title="c6">G</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>and </b><br/><a NAME="E8:70_1_1"/><i><font color="Green" title="E46">A6</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="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <font color="Maroon" title="c3">L</font>
 <b>and </b><br/><a NAME="E9:70_1_1"/><i><font color="Green" title="E47">A7</font></i>: 
 <a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <font color="Maroon" title="c3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K9" title="RLVECT_1:func.9">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c6">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="rmod_4.html#D9" target="_self" title="RMOD_4:def.9">Def9</a></i>;<br/><b>set </b><font color="Maroon" title="c7">g</font> = <font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c6">G</font>;<br/><b>set </b><font color="Maroon" title="c8">f</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c5">F</font>;<br/><b>set </b><font color="Maroon" title="c9">l</font> = <font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font>;<br/><b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>) <b>-&gt; </b>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  = <font color="Maroon" title="c5">F</font> <a href="finseq_4.html#K1" title="FINSEQ_4:func.1">&lt;-</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> $1</span>)</span>;<br/><b>consider </b><font color="Maroon" title="c10">P</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E11:70_1_1"/><i><font color="Green" title="E48">A8</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">P</font> <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="c5">F</font>
 <b>and </b><br/><a NAME="E12:70_1_1"/><i><font color="Green" title="E49">A9</font></i>: 
for <font color="Olive" title="b1">k</font> being   <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>   st <font color="Olive" title="b1">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> <font color="Maroon" title="c5">F</font></span>)</span> holds <br/><font color="Maroon" title="c10">P</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">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>)
 <b>from </b><i><a class="ref" href="finseq_1.html#S2" title="FINSEQ_1:sch.2">FINSEQ_1:sch 2</a>();<br/></i><a NAME="E13:70_1_1"/><i><font color="Green" title="E50">A10</font></i>: 
 <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E1:70_1_1"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="rmod_4.html#T59" target="_self" title="RMOD_4:th.59">Th59</a></i>;<br/><a NAME="E14:70_1_1"/><b>then </b><i><font color="Green" title="E51">A11</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">G</font> <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="c5">F</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E3:70_1_1"><i><font color="Green" title="E42">A2</font></i></a>, <a class="txt" href="rmod_4.html#E4:70_1_1"><i><font color="Green" title="E43">A3</font></i></a>, <a class="txt" href="rmod_4.html#E7:70_1_1"><i><font color="Green" title="E45">A5</font></i></a>, <a class="txt" href="rmod_4.html#E8:70_1_1"><i><font color="Green" title="E46">A6</font></i></a>, <a class="ref" href="finseq_1.html#T65" title="FINSEQ_1:th.65">FINSEQ_1:65</a></i>;<br/><a NAME="E15:70_1_1"/><i><font color="Green" title="E52">A12</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c10">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c11">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:70_1_1_1"/>
<font color="Maroon" title="c11">x</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="c10">P</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c12">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:70_1_1_1"/><i><font color="Green" title="E53">A13</font></i>: 
<font color="Maroon" title="c12">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c10">P</font>
 <b>and </b><br/><a NAME="E4:70_1_1_1"/><i><font color="Green" title="E54">A14</font></i>: 
<font color="Maroon" title="c10">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">x</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c13">y</font> = <font color="Maroon" title="c12">y</font> as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> <b>by </b><i><a class="txt" href="rmod_4.html#E3:70_1_1_1"><i><font color="Green" title="E53">A13</font></i></a>, <a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></i>;<br/>
<a NAME="E6:70_1_1_1"/><i><font color="Green" title="E55">A15</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">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> <font color="Maroon" title="c5">F</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="E7:70_1_1_1"/><i><font color="Green" title="E56">A16</font></i>: 
<font color="Maroon" title="c13">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font>
 
<b>by </b><i><a class="txt" href="rmod_4.html#E11:70_1_1"><i><font color="Green" title="E48">A8</font></i></a>, <a class="txt" href="rmod_4.html#E3:70_1_1_1"><i><font color="Green" title="E53">A13</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/>
<a NAME="E8:70_1_1_1"/>
<font color="Maroon" title="c13">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c6">G</font>
 
<b>by </b><i><a class="txt" href="rmod_4.html#E11:70_1_1"><i><font color="Green" title="E48">A8</font></i></a>, <a class="txt" href="rmod_4.html#E14:70_1_1"><i><font color="Green" title="E51">A11</font></i></a>, <a class="txt" href="rmod_4.html#E3:70_1_1_1"><i><font color="Green" title="E53">A13</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/>
<a NAME="E9:70_1_1_1"/><b>then </b>
<font color="Maroon" title="c6">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">y</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="c5">F</font>
 
<b>by </b><i><a class="txt" href="rmod_4.html#E4:70_1_1"><i><font color="Green" title="E43">A3</font></i></a>, <a class="txt" href="rmod_4.html#E8:70_1_1"><i><font color="Green" title="E46">A6</font></i></a>, <a class="txt" href="rmod_4.html#E13:70_1_1"><i><font color="Green" title="E50">A10</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E10:70_1_1_1"/><b>then </b>
( <font color="Maroon" title="c10">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F</font> <a href="finseq_4.html#K1" title="FINSEQ_4:func.1">&lt;-</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="c13">y</font></span>)</span> &amp; <font color="Maroon" title="c5">F</font> <a href="finseq_4.html#R2" title="FINSEQ_4:pred.2">just_once_values</a> <font color="Maroon" title="c6">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">y</font> )
 
<b>by </b><i><a class="txt" href="rmod_4.html#E3:70_1_1"><i><font color="Green" title="E42">A2</font></i></a>, <a class="txt" href="rmod_4.html#E12:70_1_1"><i><font color="Green" title="E49">A9</font></i></a>, <a class="txt" href="rmod_4.html#E6:70_1_1_1"><i><font color="Green" title="E55">A15</font></i></a>, <a class="txt" href="rmod_4.html#E7:70_1_1_1"><i><font color="Green" title="E56">A16</font></i></a>, <a class="ref" href="finseq_4.html#T10" title="FINSEQ_4:th.10">FINSEQ_4:10</a></i>;<br/>
<b>hence </b><a NAME="E11:70_1_1_1"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E4:70_1_1_1"><i><font color="Green" title="E54">A14</font></i></a>, <a class="ref" href="finseq_4.html#D3" title="FINSEQ_4:def.3">FINSEQ_4:def 3</a></i>;<br/>


</div><b>end;</b></div><div><i><font color="Green" title="E53">A17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c11">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>thus </b><a NAME="E1:70_1_1_2"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c6">G</font> implies ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c10">P</font> &amp; <font color="Maroon" title="c10">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:70_1_1_2_1"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c6">G</font>
 ;<br/>

<a NAME="E2:70_1_1_2_1"/><b>then </b>
<font color="Maroon" title="c11">x</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> <font color="Maroon" title="c10">P</font></span>)</span>
 
<b>by </b><i><a class="txt" href="rmod_4.html#E11:70_1_1"><i><font color="Green" title="E48">A8</font></i></a>, <a class="txt" href="rmod_4.html#E14:70_1_1"><i><font color="Green" title="E51">A11</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E3:70_1_1_2_1"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c10">P</font>
 <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="E4:70_1_1_2_1"/><b>then </b>
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c10">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font> &amp; <font color="Maroon" title="c10">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</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="c10">P</font> )
 
<b>by </b><i><a class="txt" href="rmod_4.html#E15:70_1_1"><i><font color="Green" title="E52">A12</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E5:70_1_1_2_1"/>
<font color="Maroon" title="c10">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font>
 ;<br/>


</div><b>end;</b></div><b>assume </b><a NAME="E2:70_1_1_2"/>
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c10">P</font> &amp; <font color="Maroon" title="c10">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font> )
 ;<br/><a NAME="E3:70_1_1_2"/><b>then </b>
<font color="Maroon" title="c11">x</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> <font color="Maroon" title="c10">P</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/><b>hence </b><a NAME="E4:70_1_1_2"/>
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c6">G</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E11:70_1_1"><i><font color="Green" title="E48">A8</font></i></a>, <a class="txt" href="rmod_4.html#E14:70_1_1"><i><font color="Green" title="E51">A11</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c11">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:70_1_1_3"/><i><font color="Green" title="E54">A18</font></i>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c6">G</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c12">n</font> = <font color="Maroon" title="c11">x</font> as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> <b>by </b><i><a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></i>;<br/><a NAME="E3:70_1_1_3"/>
<font color="Maroon" title="c6">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">n</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="c5">F</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E4:70_1_1"><i><font color="Green" title="E43">A3</font></i></a>, <a class="txt" href="rmod_4.html#E8:70_1_1"><i><font color="Green" title="E46">A6</font></i></a>, <a class="txt" href="rmod_4.html#E13:70_1_1"><i><font color="Green" title="E50">A10</font></i></a>, <a class="txt" href="rmod_4.html#E1:70_1_1_3"><i><font color="Green" title="E54">A18</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><a NAME="E4:70_1_1_3"/><b>then </b><i><font color="Green" title="E55">A19</font></i>: 
<font color="Maroon" title="c5">F</font> <a href="finseq_4.html#R2" title="FINSEQ_4:pred.2">just_once_values</a> <font color="Maroon" title="c6">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">n</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E3:70_1_1"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="finseq_4.html#T10" title="FINSEQ_4:th.10">FINSEQ_4:10</a></i>;<br/><a NAME="E5:70_1_1_3"/>
<font color="Maroon" title="c12">n</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> <font color="Maroon" title="c5">F</font></span>)</span>
 <b>by </b><i><a class="txt" href="rmod_4.html#E14:70_1_1"><i><font color="Green" title="E51">A11</font></i></a>, <a class="txt" href="rmod_4.html#E1:70_1_1_3"><i><font color="Green" title="E54">A18</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><b>then </b><font color="Maroon" title="c5">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">n</font></span>)</span> = 
<font color="Maroon" title="c5">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="finseq_4.html#K1" title="FINSEQ_4:func.1">&lt;-</a> <span class="p2">(<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="c12">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="rmod_4.html#E12:70_1_1"><i><font color="Green" title="E49">A9</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c6">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">n</font>
<b>by </b><i><a class="txt" href="rmod_4.html#E4:70_1_1_3"><i><font color="Green" title="E55">A19</font></i></a>, <a class="ref" href="finseq_4.html#D3" title="FINSEQ_4:def.3">FINSEQ_4:def 3</a></i>
;<br/><b>hence </b><a NAME="E7:70_1_1_3"/>
<font color="Maroon" title="c6">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span>
 ;<br/></div><b>end;</b></div><a NAME="E18:70_1_1"/><b>then </b><i><font color="Green" title="E54">A20</font></i>: 
<font color="Maroon" title="c6">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c10">P</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E16:70_1_1"><i><font color="Green" title="E53">A17</font></i></a>, <a class="ref" href="funct_1.html#T20" title="FUNCT_1:th.20">FUNCT_1:20</a></i>;<br/><a NAME="E19:70_1_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</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="c10">P</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c11">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:70_1_1_4"/><i><font color="Green" title="E55">A21</font></i>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c12">f</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">G</font>;<br/>
<a NAME="E2:70_1_1_4"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="txt" href="rmod_4.html#E3:70_1_1"><i><font color="Green" title="E42">A2</font></i></a>, <a class="txt" href="rmod_4.html#E4:70_1_1"><i><font color="Green" title="E43">A3</font></i></a>, <a class="txt" href="rmod_4.html#E8:70_1_1"><i><font color="Green" title="E46">A6</font></i></a>, <a class="txt" href="rmod_4.html#E13:70_1_1"><i><font color="Green" title="E50">A10</font></i></a>, <a class="ref" href="funct_1.html#T55" title="FUNCT_1:th.55">FUNCT_1:55</a></i>;<br/>
<b>then </b><i><font color="Green" title="E56">A22</font></i>:  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">G</font></span>)</span> = 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T47" title="RELAT_1:th.47">RELAT_1:47</a></i>
<br/>.= 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font>
<b>by </b><i><a class="txt" href="rmod_4.html#E3:70_1_1"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="funct_1.html#T55" title="FUNCT_1:th.55">FUNCT_1:55</a></i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">G</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c10">P</font>
<b>by </b><i><a class="txt" href="rmod_4.html#E18:70_1_1"><i><font color="Green" title="E54">A20</font></i></a>, <a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c10">P</font>
<b>by </b><i><a class="txt" href="rmod_4.html#E3:70_1_1"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="funct_1.html#T61" title="FUNCT_1:th.61">FUNCT_1:61</a></i>
<br/>.= 
<font color="Maroon" title="c10">P</font>
<b>by </b><i><a class="txt" href="rmod_4.html#E15:70_1_1"><i><font color="Green" title="E52">A12</font></i></a>, <a class="ref" href="relat_1.html#T79" title="RELAT_1:th.79">RELAT_1:79</a></i>
;<br/>
<b>hence </b><a NAME="E5:70_1_1_4"/>
<font color="Maroon" title="c11">x</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="c10">P</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E1:70_1_1_4"><i><font color="Green" title="E55">A21</font></i></a>, <a class="txt" href="rmod_4.html#E3:70_1_1_4"><i><font color="Green" title="E56">A22</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E20:70_1_1"/><b>then </b><i><font color="Green" title="E55">A23</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c10">P</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E15:70_1_1"><i><font color="Green" title="E52">A12</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/><a NAME="E21:70_1_1"/><i><font color="Green" title="E56">A24</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c10">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E11:70_1_1"><i><font color="Green" title="E48">A8</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/><a NAME="E22:70_1_1"/><b>then </b><i><font color="Green" title="E57">A25</font></i>: 
<font color="Maroon" title="c10">P</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>by </b><i><a class="txt" href="rmod_4.html#E20:70_1_1"><i><font color="Green" title="E55">A23</font></i></a>, <a class="ref" href="finseq_4.html#T75" title="FINSEQ_4:th.75">FINSEQ_4:75</a></i>;<br/><a NAME="E23:70_1_1"/><i><font color="Green" title="E58">A26</font></i>: 
 <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="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c5">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="c5">F</font>
 <b>by </b><i><a class="ref" href="rmod_4.html#D8" target="_self" title="RMOD_4:def.8">Def8</a></i>;<br/><a NAME="E24:70_1_1"/><b>then </b><i><font color="Green" title="E59">A27</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/><a NAME="E25:70_1_1"/>
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ;<br/><b>then reconsider </b><font color="Maroon" title="c11">P</font> = <font color="Maroon" title="c10">P</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font>, <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font> <b>by </b><i><a class="txt" href="rmod_4.html#E15:70_1_1"><i><font color="Green" title="E52">A12</font></i></a>, <a class="txt" href="rmod_4.html#E21:70_1_1"><i><font color="Green" title="E56">A24</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c12">P</font> = <font color="Maroon" title="c11">P</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c5">F</font></span>)</span>, <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c5">F</font></span>)</span> <b>by </b><i><a class="txt" href="rmod_4.html#E24:70_1_1"><i><font color="Green" title="E59">A27</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c13">Fp</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c12">P</font> as   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="ref" href="finseq_2.html#T51" title="FINSEQ_2:th.51">FINSEQ_2:51</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c14">P</font> = <font color="Maroon" title="c12">P</font> as   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c5">F</font></span>)</span> <b>by </b><i><a class="txt" href="rmod_4.html#E20:70_1_1"><i><font color="Green" title="E55">A23</font></i></a>, <a class="txt" href="rmod_4.html#E22:70_1_1"><i><font color="Green" title="E57">A25</font></i></a>, <a class="txt" href="rmod_4.html#E24:70_1_1"><i><font color="Green" title="E59">A27</font></i></a>, <a class="ref" href="funct_2.html#T83" title="FUNCT_2:th.83">FUNCT_2:83</a></i>;<br/><a NAME="E30:70_1_1"/><i><font color="Green" title="E60">A28</font></i>: 
<font color="Maroon" title="c13">Fp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c14">P</font>
 ;<br/><a NAME="E31:70_1_1"/><b>then </b><i><font color="Green" title="E61">A29</font></i>: 
 <a href="rlvect_1.html#K9" title="RLVECT_1:func.9">Sum</a> <font color="Maroon" title="c13">Fp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K9" title="RLVECT_1:func.9">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c5">F</font></span>)</span>
 <b>by </b><i><a class="ref" href="rlvect_2.html#T9" title="RLVECT_2:th.9">RLVECT_2:9</a></i>;<br/><a NAME="E32:70_1_1"/><i><font color="Green" title="E62">A30</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c13">Fp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c5">F</font></span>)</span>
 <b>by </b><i><a class="txt" href="rmod_4.html#E30:70_1_1"><i><font color="Green" title="E60">A28</font></i></a>, <a class="ref" href="finseq_2.html#T48" title="FINSEQ_2:th.48">FINSEQ_2:48</a></i>;<br/><a NAME="E33:70_1_1"/><b>then </b><i><font color="Green" title="E63">A31</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c13">Fp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c6">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="rmod_4.html#E14:70_1_1"><i><font color="Green" title="E51">A11</font></i></a>, <a class="txt" href="rmod_4.html#E23:70_1_1"><i><font color="Green" title="E58">A26</font></i></a>, <a class="ref" href="rmod_4.html#D8" target="_self" title="RMOD_4:def.8">Def8</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c15">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c16">v</font> be   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font>;<br/><b>assume </b><b>that </b><br/><a NAME="E1:70_1_1_5"/><i><font color="Green" title="E64">A32</font></i>: 
<font color="Maroon" title="c15">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c13">Fp</font>
 <b>and </b><br/><a NAME="E2:70_1_1_5"/><i><font color="Green" title="E65">A33</font></i>: 
<font color="Maroon" title="c16">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="rmod_4.html#K4" title="RMOD_4:func.4">(#)</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="c15">k</font>
 ;<br/><a NAME="E3:70_1_1_5"/><i><font color="Green" title="E66">A34</font></i>: 
<font color="Maroon" title="c15">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"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c6">G</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="rmod_4.html#E33:70_1_1"><i><font color="Green" title="E63">A31</font></i></a>, <a class="txt" href="rmod_4.html#E1:70_1_1_5"><i><font color="Green" title="E64">A32</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="E4:70_1_1_5"/><b>then </b><i><font color="Green" title="E67">A35</font></i>: 
<font color="Maroon" title="c15">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c6">G</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E14:70_1_1"><i><font color="Green" title="E51">A11</font></i></a>, <a class="txt" href="rmod_4.html#E23:70_1_1"><i><font color="Green" title="E58">A26</font></i></a>, <a class="txt" href="rmod_4.html#E32:70_1_1"><i><font color="Green" title="E62">A30</font></i></a>, <a class="txt" href="rmod_4.html#E33:70_1_1"><i><font color="Green" title="E63">A31</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="E5:70_1_1_5"/><b>then </b>
<font color="Maroon" title="c6">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">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#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><a NAME="E6:70_1_1_5"/><b>then </b>
<font color="Maroon" title="c5">F</font> <a href="finseq_4.html#R2" title="FINSEQ_4:pred.2">just_once_values</a> <font color="Maroon" title="c6">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E3:70_1_1"><i><font color="Green" title="E42">A2</font></i></a>, <a class="txt" href="rmod_4.html#E4:70_1_1"><i><font color="Green" title="E43">A3</font></i></a>, <a class="txt" href="rmod_4.html#E8:70_1_1"><i><font color="Green" title="E46">A6</font></i></a>, <a class="txt" href="rmod_4.html#E13:70_1_1"><i><font color="Green" title="E50">A10</font></i></a>, <a class="ref" href="finseq_4.html#T10" title="FINSEQ_4:th.10">FINSEQ_4:10</a></i>;<br/><a NAME="E7:70_1_1_5"/><b>then </b><i><font color="Green" title="E68">A36</font></i>: 
<font color="Maroon" title="c5">F</font> <a href="finseq_4.html#K1" title="FINSEQ_4:func.1">&lt;-</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="c15">k</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">F</font>
 <b>by </b><i><a class="ref" href="finseq_4.html#D3" title="FINSEQ_4:def.3">FINSEQ_4:def 3</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c17">i</font> = <font color="Maroon" title="c5">F</font> <a href="finseq_4.html#K1" title="FINSEQ_4:func.1">&lt;-</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="c15">k</font></span>)</span> as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> <b>by </b><i><a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></i>;<br/><a NAME="E9:70_1_1_5"/><i><font color="Green" title="E69">A37</font></i>: 
<font color="Maroon" title="c15">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c6">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="rmod_4.html#E3:70_1_1_5"><i><font color="Green" title="E66">A34</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="E10:70_1_1_5"/><i><font color="Green" title="E70">A38</font></i>: 
<font color="Maroon" title="c15">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c14">P</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E11:70_1_1"><i><font color="Green" title="E48">A8</font></i></a>, <a class="txt" href="rmod_4.html#E23:70_1_1"><i><font color="Green" title="E58">A26</font></i></a>, <a class="txt" href="rmod_4.html#E32:70_1_1"><i><font color="Green" title="E62">A30</font></i></a>, <a class="txt" href="rmod_4.html#E33:70_1_1"><i><font color="Green" title="E63">A31</font></i></a>, <a class="txt" href="rmod_4.html#E3:70_1_1_5"><i><font color="Green" title="E66">A34</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><i><font color="Green" title="E71">A39</font></i>: <font color="Maroon" title="c6">G</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c15">k</font> = 
<font color="Maroon" title="c6">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font>
<b>by </b><i><a class="txt" href="rmod_4.html#E4:70_1_1_5"><i><font color="Green" title="E67">A35</font></i></a>, <a class="ref" href="finseq_4.html#D4" title="FINSEQ_4:def.4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon" title="c5">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font></span>)</span>
<b>by </b><i><a class="txt" href="rmod_4.html#E18:70_1_1"><i><font color="Green" title="E54">A20</font></i></a>, <a class="txt" href="rmod_4.html#E10:70_1_1_5"><i><font color="Green" title="E70">A38</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon" title="c5">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">i</font>
<b>by </b><i><a class="txt" href="rmod_4.html#E12:70_1_1"><i><font color="Green" title="E49">A9</font></i></a>, <a class="txt" href="rmod_4.html#E23:70_1_1"><i><font color="Green" title="E58">A26</font></i></a>, <a class="txt" href="rmod_4.html#E32:70_1_1"><i><font color="Green" title="E62">A30</font></i></a>, <a class="txt" href="rmod_4.html#E33:70_1_1"><i><font color="Green" title="E63">A31</font></i></a>, <a class="txt" href="rmod_4.html#E3:70_1_1_5"><i><font color="Green" title="E66">A34</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c5">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c17">i</font>
<b>by </b><i><a class="txt" href="rmod_4.html#E7:70_1_1_5"><i><font color="Green" title="E68">A36</font></i></a>, <a class="ref" href="finseq_4.html#D4" title="FINSEQ_4:def.4">FINSEQ_4:def 4</a></i>
;<br/><a NAME="E12:70_1_1_5"/>
<font color="Maroon" title="c17">i</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="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c5">F</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="rmod_4.html#E23:70_1_1"><i><font color="Green" title="E58">A26</font></i></a>, <a class="txt" href="rmod_4.html#E7:70_1_1_5"><i><font color="Green" title="E68">A36</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="E13:70_1_1_5"/><b>then </b><i><font color="Green" title="E72">A40</font></i>: 
<font color="Maroon" title="c17">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c5">F</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/><b>thus </b><font color="Maroon" title="c13">Fp</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font></span>)</span>
<b>by </b><i><a class="txt" href="rmod_4.html#E10:70_1_1_5"><i><font color="Green" title="E70">A38</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"><span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="rmod_4.html#K4" title="RMOD_4:func.4">(#)</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="finseq_4.html#K1" title="FINSEQ_4:func.1">&lt;-</a> <span class="p2">(<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="c15">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="rmod_4.html#E12:70_1_1"><i><font color="Green" title="E49">A9</font></i></a>, <a class="txt" href="rmod_4.html#E23:70_1_1"><i><font color="Green" title="E58">A26</font></i></a>, <a class="txt" href="rmod_4.html#E32:70_1_1"><i><font color="Green" title="E62">A30</font></i></a>, <a class="txt" href="rmod_4.html#E33:70_1_1"><i><font color="Green" title="E63">A31</font></i></a>, <a class="txt" href="rmod_4.html#E3:70_1_1_5"><i><font color="Green" title="E66">A34</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c17">i</font></span>)</span> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</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="c5">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c17">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="rmod_4.html#E13:70_1_1_5"><i><font color="Green" title="E72">A40</font></i></a>, <a class="ref" href="rmod_4.html#D8" target="_self" title="RMOD_4:def.8">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c17">i</font></span>)</span> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</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="c5">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c17">i</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c4">a</font></span>)</span>
<b>by </b><i><a class="ref" href="rmod_4.html#D12" target="_self" title="RMOD_4:def.12">Def12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c17">i</font></span>)</span> <a href="vectsp_2.html#K6" title="VECTSP_2: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="c5">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c17">i</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c4">a</font>
<b>by </b><i><a class="ref" href="vectsp_2.html#D23" title="VECTSP_2:def.23">VECTSP_2:def 23</a></i>
<br/>.= 
<font color="Maroon" title="c16">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c4">a</font>
<b>by </b><i><a class="txt" href="rmod_4.html#E2:70_1_1_5"><i><font color="Green" title="E65">A33</font></i></a>, <a class="txt" href="rmod_4.html#E9:70_1_1_5"><i><font color="Green" title="E69">A37</font></i></a>, <a class="txt" href="rmod_4.html#E11:70_1_1_5"><i><font color="Green" title="E71">A39</font></i></a>, <a class="ref" href="rmod_4.html#D8" target="_self" title="RMOD_4:def.8">Def8</a></i>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E35:70_1_1"/>
 <a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c4">a</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E5:70_1_1"><i><font color="Green" title="E44">A4</font></i></a>, <a class="txt" href="rmod_4.html#E9:70_1_1"><i><font color="Green" title="E47">A7</font></i></a>, <a class="txt" href="rmod_4.html#E31:70_1_1"><i><font color="Green" title="E61">A29</font></i></a>, <a class="txt" href="rmod_4.html#E33:70_1_1"><i><font color="Green" title="E63">A31</font></i></a>, <a class="ref" href="rmod_4.html#T1" target="_self" title="RMOD_4:th.1">Th1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_2"><b>suppose </b></a><a NAME="E1:70_1_2"/><i><font color="Green" title="E41">A41</font></i>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">R</font>
 ;<br/><div class="add"><b>hence </b> <a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c4">a</font></span>)</span> = 
 <a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K3" title="RMOD_4:func.3">ZeroLC</a> <font color="Maroon" title="c2">V</font></span>)</span>
<b>by </b><i><a class="ref" href="rmod_4.html#T60" target="_self" title="RMOD_4:th.60">Th60</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c2">V</font>
<b>by </b><i><a class="txt" href="rmod_4.html#E49"><i><font color="Green" title="E22">Lm3</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c4">a</font>
<b>by </b><i><a class="txt" href="rmod_4.html#E1:70_1_2"><i><font color="Green" title="E41">A41</font></i></a>, <a class="ref" href="mod_1.html#T37" title="MOD_1:th.37">MOD_1:37</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
