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<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">n</font>, <font color="Maroon" title="c3">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c4">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/><b>let </b><font color="Maroon" title="c5">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">K</font>;<br/><b>let </b><font color="Maroon" title="c6">L</font> be    <a href="vectsp_6.html#M1" title="VECTSP_6:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">n</font> <a href="prvect_1.html#K7" title="PRVECT_1:func.7">-VectSp_over</a> <font color="Maroon" title="c4">K</font>;<br/><b>let </b><font color="Maroon" title="c7">M</font> be   <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c4">K</font>;<br/>













<b>assume </b><b>that </b><br/><a NAME="E1:129"/><i><font color="Green" title="E105">A1</font></i>: 
<font color="Maroon" title="c3">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> <font color="Maroon" title="c7">M</font></span>)</span>
 <b>and </b><br/><a NAME="E2:129"/><i><font color="Green" title="E106">A2</font></i>: 
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font></span>)</span>
 ;<br/>

<b>set </b><font color="Maroon" title="c8">MX</font> =  <a href="matrix13.html#K10" title="MATRIX13:func.10">MX2FinS</a> <font color="Maroon" title="c7">M</font>;<br/>
<b>set </b><font color="Maroon" title="c9">LM</font> = <font color="Maroon" title="c6">L</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <span class="p1">(<span class="default"><a href="matrix13.html#K10" title="MATRIX13:func.10">MX2FinS</a> <font color="Maroon" title="c7">M</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c10">FLM</font> =  <a href="matrix13.html#K9" title="MATRIX13:func.9">FinS2MX</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">L</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <span class="p2">(<span class="default"><a href="matrix13.html#K10" title="MATRIX13:func.10">MX2FinS</a> <font color="Maroon" title="c7">M</font></span>)</span></span>)</span>;<br/>
<a NAME="E3:129"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">L</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <span class="p2">(<span class="default"><a href="matrix13.html#K10" title="MATRIX13:func.10">MX2FinS</a> <font color="Maroon" title="c7">M</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> <font color="Maroon" title="c7">M</font> &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <font color="Maroon" title="c7">M</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font> )
 
<b>by </b><i><a class="txt" href="matrix13.html#E1:129"><i><font color="Green" title="E105">A1</font></i></a>, <a class="ref" href="vectsp_6.html#D8" title="VECTSP_6:def.8">VECTSP_6:def 8</a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a>, <a class="ref" href="matrix_1.html#D3" title="MATRIX_1:def.3">MATRIX_1:def 3</a></i>;<br/>
<a NAME="E4:129"/><b>then </b><i><font color="Green" title="E107">A3</font></i>: 
(  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrix13.html#K9" title="MATRIX13:func.9">FinS2MX</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">L</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <span class="p3">(<span class="default"><a href="matrix13.html#K10" title="MATRIX13:func.10">MX2FinS</a> <font color="Maroon" title="c7">M</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix13.html#K9" title="MATRIX13:func.9">FinS2MX</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">L</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <span class="p3">(<span class="default"><a href="matrix13.html#K10" title="MATRIX13:func.10">MX2FinS</a> <font color="Maroon" title="c7">M</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> &amp; <font color="Maroon" title="c7">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix13.html#K10" title="MATRIX13:func.10">MX2FinS</a> <font color="Maroon" title="c7">M</font></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c3">i</font> &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <span class="p1">(<span class="default"><a href="matrix13.html#K9" title="MATRIX13:func.9">FinS2MX</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">L</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <span class="p3">(<span class="default"><a href="matrix13.html#K10" title="MATRIX13:func.10">MX2FinS</a> <font color="Maroon" title="c7">M</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c7">M</font>,<font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> &amp;  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c7">M</font>,<font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix13.html#K8" title="MATRIX13:func.8">lines</a> <font color="Maroon" title="c7">M</font> )
 
<b>by </b><i><a class="txt" href="matrix13.html#E1:129"><i><font color="Green" title="E105">A1</font></i></a>, <a class="ref" href="matrix_2.html#T10" title="MATRIX_2:th.10">MATRIX_2:10</a>, <a class="ref" href="finseq_4.html#D4" title="FINSEQ_4:def.4">FINSEQ_4:def 4</a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a>, <a class="ref" href="matrix13.html#T103" target="_self" title="MATRIX13:th.103">TT103</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c11">L</font> =  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c7">M</font>,<font color="Maroon" title="c3">i</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">K</font> <b>by </b><i><a class="ref" href="matrix13.html#T102" target="_self" title="MATRIX13:th.102">TT102</a></i>;<br/>
<b>thus </b> <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrix13.html#K9" title="MATRIX13:func.9">FinS2MX</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">L</font> <a href="vectsp_6.html#K3" title="VECTSP_6:func.3">(#)</a> <span class="p3">(<span class="default"><a href="matrix13.html#K10" title="MATRIX13:func.10">MX2FinS</a> <font color="Maroon" title="c7">M</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">i</font> = 
<font color="Maroon" title="c5">a</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix13.html#K10" title="MATRIX13:func.10">MX2FinS</a> <font color="Maroon" title="c7">M</font></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c3">i</font></span>)</span>
<b>by </b><i><a class="txt" href="matrix13.html#E2:129"><i><font color="Green" title="E106">A2</font></i></a>, <a class="txt" href="matrix13.html#E4:129"><i><font color="Green" title="E107">A3</font></i></a>, <a class="ref" href="vectsp_6.html#D8" title="VECTSP_6:def.8">VECTSP_6:def 8</a></i>
<br/>.= 
<font color="Maroon" title="c5">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <font color="Maroon" title="c11">L</font>
<b>by </b><i><a class="txt" href="matrix13.html#E4:129"><i><font color="Green" title="E107">A3</font></i></a>, <a class="ref" href="matrix13.html#T102" target="_self" title="MATRIX13:th.102">TT102</a></i>
<br/>.= 
<font color="Maroon" title="c5">a</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c7">M</font>,<font color="Maroon" title="c3">i</font></span>)</span>

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