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<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</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">a</font> be   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R</font>;<br/><b>let </b><font color="Maroon" title="c4">F</font>, <font color="Maroon" title="c5">G</font> be   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c2">V</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:3"/><i><font color="Green" title="E4">A1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">F</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">G</font>
 <b>and </b><br/><a NAME="E2:3"/><i><font color="Green" title="E5">A2</font></i>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">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="c4">F</font> holds <br/><font color="Maroon" title="c5">G</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> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c3">a</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c7">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="E1:3_1"/><i><font color="Green" title="E6">A3</font></i>: 
<font color="Maroon" title="c6">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="c5">G</font>
 <b>and </b><br/><a NAME="E2:3_1"/><i><font color="Green" title="E7">A4</font></i>: 
<font color="Maroon" title="c7">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">k</font>
 ;<br/><a NAME="E3:3_1"/><i><font color="Green" title="E8">A5</font></i>: 
<font color="Maroon" title="c6">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="c4">F</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E1:3"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="rmod_4.html#E1:3_1"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/><a NAME="E4:3_1"/><b>then </b>
<font color="Maroon" title="c7">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c6">k</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E2:3_1"><i><font color="Green" title="E7">A4</font></i></a>, <a class="ref" href="finseq_4.html#D4" title="FINSEQ_4:def.4">FINSEQ_4:def 4</a></i>;<br/><b>hence </b><a NAME="E5:3_1"/>
<font color="Maroon" title="c5">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E2:3"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="rmod_4.html#E3:3_1"><i><font color="Green" title="E8">A5</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:3"/>
 <a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <font color="Maroon" title="c5">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E1:3"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="rmod_4.html#T1" target="_self" title="RMOD_4:th.1">Th1</a></i>;<br/>


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