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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font><br/> for <font color="Olive" title="b2">V1</font>, <font color="Olive" title="b3">V2</font> being <a href="matrlin.html#V2" title="MATRLIN:attr.2">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="b4">b1</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b2">V1</font><br/> for <font color="Olive" title="b5">B2</font> being  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Olive" title="b3">V2</font><br/> for <font color="Olive" title="b6">A</font> being  <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b4">b1</font>, <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b5">B2</font>,<font color="Maroon" title="c1">K</font> holds  <font color="Olive" title="b1">a</font> <a href="matrlin.html#K6" title="MATRLIN:func.6">*</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Olive" title="b6">A</font>,<font color="Olive" title="b4">b1</font>,<font color="Olive" title="b5">B2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <font color="Olive" title="b6">A</font></span>)</span>,<font color="Olive" title="b4">b1</font>,<font color="Olive" title="b5">B2</font></span><br/><b>let </b><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">V1</font>, <font color="Olive" title="b2">V2</font> being <a href="matrlin.html#V2" title="MATRLIN:attr.2">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="b3">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="b4">B2</font> being  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Olive" title="b2">V2</font><br/> for <font color="Olive" title="b5">A</font> being  <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">b1</font>, <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b4">B2</font>,<font color="Maroon" title="c1">K</font> holds  <font color="Maroon" title="c2">a</font> <a href="matrlin.html#K6" title="MATRLIN:func.6">*</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Olive" title="b5">A</font>,<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">B2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <font color="Olive" title="b5">A</font></span>)</span>,<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">B2</font></span><br/><b>let </b><font color="Maroon" title="c3">V1</font>, <font color="Maroon" title="c4">V2</font> be  <a href="matrlin.html#V2" title="MATRLIN:attr.2">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:()"><i><font color="Red">::  thesis: </font></i></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="c3">V1</font><br/> for <font color="Olive" title="b2">B2</font> being  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c4">V2</font><br/> for <font color="Olive" title="b3">A</font> being  <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">b1</font>, <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">B2</font>,<font color="Maroon" title="c1">K</font> holds  <font color="Maroon" title="c2">a</font> <a href="matrlin.html#K6" title="MATRLIN:func.6">*</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Olive" title="b3">A</font>,<font color="Olive" title="b1">b1</font>,<font color="Olive" title="b2">B2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <font color="Olive" title="b3">A</font></span>)</span>,<font color="Olive" title="b1">b1</font>,<font color="Olive" title="b2">B2</font></span><br/><b>let </b><font color="Maroon" title="c5">b1</font> be    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c3">V1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">B2</font> being  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c4">V2</font><br/> for <font color="Olive" title="b2">A</font> being  <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">b1</font>, <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">B2</font>,<font color="Maroon" title="c1">K</font> holds  <font color="Maroon" title="c2">a</font> <a href="matrlin.html#K6" title="MATRLIN:func.6">*</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Olive" title="b2">A</font>,<font color="Maroon" title="c5">b1</font>,<font color="Olive" title="b1">B2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <font color="Olive" title="b2">A</font></span>)</span>,<font color="Maroon" title="c5">b1</font>,<font color="Olive" title="b1">B2</font></span><br/><b>let </b><font color="Maroon" title="c6">B2</font> be   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c4">V2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">b1</font>, <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">B2</font>,<font color="Maroon" title="c1">K</font> holds  <font color="Maroon" title="c2">a</font> <a href="matrlin.html#K6" title="MATRLIN:func.6">*</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Olive" title="b1">A</font>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">B2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <font color="Olive" title="b1">A</font></span>)</span>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">B2</font></span><br/><b>let </b><font color="Maroon" title="c7">A</font> be   <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">b1</font>, <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">B2</font>,<font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="matrlin.html#K6" title="MATRLIN:func.6">*</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">B2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">B2</font></span><br/>













<b>set </b><font color="Maroon" title="c8">aA</font> = <font color="Maroon" title="c2">a</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <font color="Maroon" title="c7">A</font>;<br/>
<b>set </b><font color="Maroon" title="c9">aM</font> =  <a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">B2</font>;<br/>
<b>set </b><font color="Maroon" title="c10">M</font> =  <a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">B2</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1"><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">V1</font> implies <span class="p1">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">B2</font></span>)</span> <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> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="matrlin.html#K6" title="MATRLIN:func.6">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">B2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> )</span><br/><b>assume </b><a NAME="E1:49_1"/><i><font color="Green" title="E29">A1</font></i>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">V1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">B2</font></span>)</span> <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> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="matrlin.html#K6" title="MATRLIN:func.6">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">B2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span><br/><b>reconsider </b><font color="Maroon" title="c12">v</font> = <font color="Maroon" title="c11">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">V1</font> <b>by </b><i><a class="txt" href="matrlin2.html#E1:49_1"><i><font color="Green" title="E29">A1</font></i></a></i>;<br/><b>set </b><font color="Maroon" title="c13">L</font> =  <a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span>;<br/><b>set </b><font color="Maroon" title="c14">amA</font> =  <a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon" title="c6">B2</font>;<br/><b>set </b><font color="Maroon" title="c15">mA</font> =  <a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span>,<font color="Maroon" title="c6">B2</font>;<br/><a NAME="E3:49_1"/><i><font color="Green" title="E30">A2</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></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> <span class="p1">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">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="c5">b1</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">A</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">b1</font> )
 <b>by </b><i><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a>, <a class="ref" href="matrix_1.html#D3" title="MATRIX_1:def.3">MATRIX_1:def 3</a>, <a class="ref" href="matrlin.html#D9" title="MATRLIN:def.9">MATRLIN:def 9</a></i>;<br/><a NAME="E4:49_1"/><b>then </b><i><font color="Green" title="E31">A3</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"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="ref" href="matrix_3.html#D4" title="MATRIX_3:def.4">MATRIX_3:def 4</a></i>;<br/><a NAME="E5:49_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span></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> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span>
 <b>by </b><i><a class="ref" href="matrixr1.html#T16" title="MATRIXR1:th.16">MATRIXR1:16</a></i>;<br/><a NAME="E6:49_1"/><b>then </b><i><font color="Green" title="E32">A4</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon" title="c6">B2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">B2</font></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span></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> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span>,<font color="Maroon" title="c6">B2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">B2</font></span>)</span> )
 <b>by </b><i><a class="txt" href="matrlin2.html#E7"><i><font color="Green" title="E4">Lm1</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/><a NAME="E7:49_1"/><b>then </b><i><font color="Green" title="E33">A5</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span>,<font color="Maroon" title="c6">B2</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> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon" title="c6">B2</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/><div><i><font color="Green" title="E34">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c16">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c16">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"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span>,<font color="Maroon" title="c6">B2</font></span>)</span> implies <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon" title="c6">B2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span>,<font color="Maroon" title="c6">B2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">k</font></span>)</span> )</span><br/><b>assume </b><a NAME="E1:49_1_1"/><i><font color="Green" title="E35">A7</font></i>: 
<font color="Maroon" title="c16">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"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span>,<font color="Maroon" title="c6">B2</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon" title="c6">B2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span>,<font color="Maroon" title="c6">B2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">k</font></span>)</span></span><br/><a NAME="E2:49_1_1"/><i><font color="Green" title="E36">A8</font></i>: 
( <font color="Maroon" title="c16">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"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span> &amp; <font color="Maroon" title="c16">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="c2">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span></span>)</span> &amp; <font color="Maroon" title="c16">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">B2</font> )
 <b>by </b><i><a class="txt" href="matrlin2.html#E1:49_1_1"><i><font color="Green" title="E35">A7</font></i></a>, <a class="txt" href="matrlin2.html#E6:49_1"><i><font color="Green" title="E32">A4</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E3:49_1_1"/><b>then </b><i><font color="Green" title="E37">A9</font></i>: 
( <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">k</font> &amp; <font color="Maroon" title="c6">B2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">B2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">k</font> &amp; <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span>,<font color="Maroon" title="c6">B2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span>,<font color="Maroon" title="c6">B2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">k</font> )
 <b>by </b><i><a class="txt" href="matrlin2.html#E1:49_1_1"><i><font color="Green" title="E35">A7</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>;<br/><a NAME="E4:49_1_1"/><b>then </b><i><font color="Green" title="E38">A10</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="matrlin2.html#E2:49_1_1"><i><font color="Green" title="E36">A8</font></i></a>, <a class="ref" href="fvsum_1.html#T62" title="FVSUM_1:th.62">FVSUM_1:62</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon" title="c6">B2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">k</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">k</font></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">B2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">k</font></span>)</span>
<b>by </b><i><a class="txt" href="matrlin2.html#E6:49_1"><i><font color="Green" title="E32">A4</font></i></a>, <a class="txt" href="matrlin2.html#E1:49_1_1"><i><font color="Green" title="E35">A7</font></i></a>, <a class="txt" href="matrlin2.html#E3:49_1_1"><i><font color="Green" title="E37">A9</font></i></a>, <a class="txt" href="matrlin2.html#E4:49_1_1"><i><font color="Green" title="E38">A10</font></i></a>, <a class="ref" href="funcop_1.html#T28" title="FUNCOP_1:th.28">FUNCOP_1:28</a></i>
<br/>.= 
<font color="Maroon" title="c2">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">k</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">B2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>
<br/>.= 
<font color="Maroon" title="c2">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span>,<font color="Maroon" title="c6">B2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">k</font></span>)</span>
<b>by </b><i><a class="txt" href="matrlin2.html#E1:49_1_1"><i><font color="Green" title="E35">A7</font></i></a>, <a class="txt" href="matrlin2.html#E3:49_1_1"><i><font color="Green" title="E37">A9</font></i></a>, <a class="ref" href="funcop_1.html#T28" title="FUNCOP_1:th.28">FUNCOP_1:28</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>thus </b><span class="p1">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">B2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> = 
 <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p5">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <font color="Maroon" title="c7">A</font></span>)</span></span>)</span>,1</span>)</span>,<font color="Maroon" title="c6">B2</font></span>)</span>
<b>by </b><i><a class="ref" href="matrlin2.html#D3" target="_self" title="MATRLIN2:def.3">Def3</a></i>
<br/>.= 
 <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span></span>)</span>,1</span>)</span>,<font color="Maroon" title="c6">B2</font></span>)</span>
<b>by </b><i><a class="txt" href="matrlin2.html#E3:49_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="matrixr1.html#T22" title="MATRIXR1:th.22">MATRIXR1:22</a></i>
<br/>.= 
 <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon" title="c6">B2</font></span>)</span>
<b>by </b><i><a class="txt" href="matrlin2.html#E4:49_1"><i><font color="Green" title="E31">A3</font></i></a>, <a class="ref" href="matrixr1.html#T20" title="MATRIXR1:th.20">MATRIXR1:20</a></i>
<br/>.= 
<font color="Maroon" title="c2">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p0">(<span class="default"><font color="Maroon" title="c12">v</font> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c5">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,1</span>)</span>,<font color="Maroon" title="c6">B2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrlin2.html#E7:49_1"><i><font color="Green" title="E33">A5</font></i></a>, <a class="txt" href="matrlin2.html#E8:49_1"><i><font color="Green" title="E34">A6</font></i></a>, <a class="ref" href="vectsp_3.html#T10" title="VECTSP_3:th.10">VECTSP_3:10</a></i>
<br/>.= 
<font color="Maroon" title="c2">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">B2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">v</font></span>)</span>
<b>by </b><i><a class="ref" href="matrlin2.html#D3" target="_self" title="MATRLIN2:def.3">Def3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="matrlin.html#K6" title="MATRLIN:func.6">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">B2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font>
<b>by </b><i><a class="ref" href="matrlin.html#D6" title="MATRLIN:def.6">MATRLIN:def 6</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:49"/>
<font color="Maroon" title="c2">a</font> <a href="matrlin.html#K6" title="MATRLIN:func.6">*</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">B2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</a> <font color="Maroon" title="c7">A</font></span>)</span>,<font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">B2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18" title="FUNCT_2:th.18">FUNCT_2:18</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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