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<span class="kw">set </span><font color="Maroon" title="c7">Mx</font> =  <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>);<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:43_1_1_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:43_1_1_1_1"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>) is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  &amp;  <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>) is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  )</span><br/><div class="add"><div><span class="lab"><font color="Green" title="E27">A2</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">a</font> be   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">v1</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V1</font> holds  <span class="p1">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Olive" title="b1">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">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#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">v1</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c9">v1</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">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#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> = 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">V2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43_1_1_1_1"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="matrlin2.html#T33" target="_self" title="MATRLIN2:th.33">Th33</a></span>
<br/>.= 
<font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">V2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T14" title="VECTSP_1:th.14">VECTSP_1:14</a></span>
<br/>.= 
<font color="Maroon" title="c8">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#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">v1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43_1_1_1_1"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="matrlin2.html#T33" target="_self" title="MATRLIN2:th.33">Th33</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">v1</font>, <font color="Maroon" title="c9">w1</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">v1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">w1</font></span>)</span></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> = 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">V2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43_1_1_1_1"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="matrlin2.html#T33" target="_self" title="MATRLIN2:th.33">Th33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">V2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">V2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D4" title="RLVECT_1:def.4">RLVECT_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">v1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">V2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43_1_1_1_1"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="matrlin2.html#T33" target="_self" title="MATRLIN2:th.33">Th33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">v1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">w1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43_1_1_1_1"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="matrlin2.html#T33" target="_self" title="MATRLIN2:th.33">Th33</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E4:43_1_1_1_1"/><span class="kw">then </span>
(  <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>) is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  &amp;  <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>) is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43_1_1_1_1"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="grcat_1.html#D8" title="GRCAT_1:def.8">GRCAT_1:def 8</a>, <a class="ref" href="mod_2.html#D2" title="MOD_2:def.2">MOD_2:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E5:43_1_1_1_1"/>
(  <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>) is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  &amp;  <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>) is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:43_1_1_1_2"/><span class="lab"><font color="Green" title="E26">A3</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>) is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  &amp;  <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>) is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  )</span><br/><div class="add"><div><span class="lab"><font color="Green" title="E27">A4</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">v1</font>, <font color="Maroon" title="c9">w1</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">v1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">w1</font></span>)</span></span><br/><span class="kw">set </span><font color="Maroon" title="c10">vb</font> = <font color="Maroon" title="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font>;<br/><span class="kw">set </span><font color="Maroon" title="c11">wb</font> = <font color="Maroon" title="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font>;<br/><span class="kw">set </span><font color="Maroon" title="c12">vwb</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font>;<br/><span class="kw">set </span><font color="Maroon" title="c13">Lvw</font> =  <a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c14">Lv</font> =  <a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c15">Lw</font> =  <a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c16">LLvw</font> =  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</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"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1);<br/><span class="kw">set </span><font color="Maroon" title="c17">LLv</font> =  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1);<br/><span class="kw">set </span><font color="Maroon" title="c18">LLw</font> =  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1);<br/><a NAME="E1:43_1_1_1_2_1"/><span class="lab"><font color="Green" title="E28">A5</font></span>: 
 <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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T23" title="MATRIX_1:th.23">MATRIX_1:23</a></span>;<br/><a NAME="E2:43_1_1_1_2_1"/><span class="lab"><font color="Green" title="E29">A6</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">b1</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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D7" title="MATRLIN:def.7">MATRLIN:def 7</a></span>;<br/><a NAME="E3:43_1_1_1_2_1"/><span class="lab"><font color="Green" title="E30">A7</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">M</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="c4">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43_1_1_1_2"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="ref" href="matrix_1.html#T23" title="MATRIX_1:th.23">MATRIX_1:23</a></span>;<br/><a NAME="E4:43_1_1_1_2_1"/><span class="lab"><font color="Green" title="E31">A8</font></span>: 
 <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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T23" title="MATRIX_1:th.23">MATRIX_1:23</a></span>;<br/><a NAME="E5:43_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A9</font></span>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c6">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="txt" href="#E2:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="ref" href="matrix_3.html#D4" title="MATRIX_3:def.4">MATRIX_3:def 4</a></span>;<br/><a NAME="E6:43_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A10</font></span>: 
 <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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c6">M</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>;<br/><a NAME="E7:43_1_1_1_2_1"/><span class="lab"><font color="Green" title="E34">A11</font></span>: 
 <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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T23" title="MATRIX_1:th.23">MATRIX_1:23</a></span>;<br/><a NAME="E8:43_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A12</font></span>: 
 <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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="txt" href="#E3:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="txt" href="#E2:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="ref" href="matrix_3.html#D4" title="MATRIX_3:def.4">MATRIX_3:def 4</a></span>;<br/><a NAME="E9:43_1_1_1_2_1"/><span class="lab"><font color="Green" title="E36">A13</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">b1</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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D7" title="MATRLIN:def.7">MATRLIN:def 7</a></span>;<br/><a NAME="E10:43_1_1_1_2_1"/>
(  <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"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">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"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">b1</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="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T23" title="MATRIX_1:th.23">MATRIX_1:23</a>, <a class="ref" href="matrlin.html#D7" title="MATRLIN:def.7">MATRLIN:def 7</a></span>;<br/><a NAME="E11:43_1_1_1_2_1"/><span class="kw">then </span>
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</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"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c6">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="ref" href="matrix_3.html#D4" title="MATRIX_3:def.4">MATRIX_3:def 4</a></span>;<br/><a NAME="E12:43_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A14</font></span>: 
 <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"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c6">M</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>;<br/><span class="lab"><font color="Green" title="E38">A15</font></span>:  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> = 
<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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</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="c5">B2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="matrlin2.html#E7"><span class="lab"><font color="Green" title="E4">Lm1</font></span></a></span>
<br/>.= 
<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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</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="c5">B2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E37">A14</font></span></a>, <a class="txt" href="#E6:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E33">A10</font></span></a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="matrlin2.html#E7"><span class="lab"><font color="Green" title="E4">Lm1</font></span></a></span>
;<br/><a NAME="E14:43_1_1_1_2_1"/><span class="lab"><font color="Green" title="E39">A16</font></span>: 
 <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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T23" title="MATRIX_1:th.23">MATRIX_1:23</a></span>;<br/><a NAME="E15:43_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A17</font></span>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c6">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="txt" href="#E9:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="ref" href="matrix_3.html#D4" title="MATRIX_3:def.4">MATRIX_3:def 4</a></span>;<br/><a NAME="E16:43_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A18</font></span>: 
 <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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c6">M</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>;<br/><span class="lab"><font color="Green" title="E42">A19</font></span>:  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> = 
<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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</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="c5">B2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="matrlin2.html#E7"><span class="lab"><font color="Green" title="E4">Lm1</font></span></a></span>
<br/>.= 
<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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</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="c5">B2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E37">A14</font></span></a>, <a class="txt" href="#E16:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E41">A18</font></span></a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="matrlin2.html#E7"><span class="lab"><font color="Green" title="E4">Lm1</font></span></a></span>
;<br/><a NAME="E18:43_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A20</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">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#K5" title="MATRLIN:func.5">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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></span>;<br/> <a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span> = 
 <a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T17" target="_self" title="MATRLIN2:th.17">Th17</a></span>
<br/>.= 
<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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="#E9:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="ref" href="matrix15.html#T27" title="MATRIX15:th.27">MATRIX15:27</a></span>
;<br/><a NAME="E20:43_1_1_1_2_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43_1_1_1_2"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E7:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E34">A11</font></span></a>, <a class="txt" href="#E4:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="txt" href="#E1:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E14:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E39">A16</font></span></a>, <a class="txt" href="#E3:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="txt" href="#E2:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="#E9:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="ref" href="matrix_4.html#T63" title="MATRIX_4:th.63">MATRIX_4:63</a></span>;<br/><a NAME="E21:43_1_1_1_2_1"/><span class="kw">then </span>
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</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"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1) <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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E35">A12</font></span></a>, <a class="txt" href="#E5:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E32">A9</font></span></a>, <a class="txt" href="#E15:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E40">A17</font></span></a>, <a class="txt" href="matrlin2.html#E41"><span class="lab"><font color="Green" title="E25">Lm5</font></span></a></span>;<br/><a NAME="E22:43_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A21</font></span>: 
 <a href="matrlin.html#K5" title="MATRLIN:func.5">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"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T7" target="_self" title="MATRLIN2:th.7">Th7</a></span>;<br/><div><span class="lab"><font color="Green" title="E45">A22</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1_1_2_1_4"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">i</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">i</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#K5" title="MATRLIN:func.5">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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> implies <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c19">i</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c19">i</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:43_1_1_1_2_1_4"/><span class="lab"><font color="Green" title="E46">A23</font></span>: 
<font color="Maroon" title="c19">i</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#K5" title="MATRLIN:func.5">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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c19">i</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c19">i</font></span>)</span></span><br/><a NAME="E2:43_1_1_1_2_1_4"/>
( <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c19">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">i</font> &amp; <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c19">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">i</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E17:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E42">A19</font></span></a>, <a class="txt" href="#E1:43_1_1_1_2_1_4"><span class="lab"><font color="Green" title="E46">A23</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/><span class="kw">hence </span><a NAME="E3:43_1_1_1_2_1_4"/>
<span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c19">i</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c19">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E44">A21</font></span></a>, <a class="txt" href="#E13:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E1:43_1_1_1_2_1_4"><span class="lab"><font color="Green" title="E46">A23</font></span></a>, <a class="ref" href="fvsum_1.html#T17" title="FVSUM_1:th.17">FVSUM_1:17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E24:43_1_1_1_2_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">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#K5" title="MATRLIN:func.5">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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></span>;<br/><a NAME="E25:43_1_1_1_2_1"/><span class="kw">then </span>
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E43">A20</font></span></a>, <a class="txt" href="#E23:43_1_1_1_2_1"><span class="lab"><font color="Green" title="E45">A22</font></span></a>, <a class="ref" href="rlvect_2.html#T2" title="RLVECT_2:th.2">RLVECT_2:2</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c9">w1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c8">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#D3" target="_self" title="MATRLIN2:def.3">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">v1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c9">w1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#D3" target="_self" title="MATRLIN2:def.3">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">v1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">w1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#D3" target="_self" title="MATRLIN2:def.3">Def3</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1_1_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">a</font> be   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">v1</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V1</font> holds  <span class="p1">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Olive" title="b1">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">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#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">v1</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c9">v1</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">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#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><br/><span class="kw">set </span><font color="Maroon" title="c10">vb</font> = <font color="Maroon" title="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font>;<br/><span class="kw">set </span><font color="Maroon" title="c11">avb</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font>;<br/><span class="kw">set </span><font color="Maroon" title="c12">Lav</font> =  <a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c13">Lv</font> =  <a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c14">LLav</font> =  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</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"><span class="p4">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1);<br/><span class="kw">set </span><font color="Maroon" title="c15">LLv</font> =  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1);<br/><a NAME="E1:43_1_1_1_2_2"/><span class="lab"><font color="Green" title="E28">A24</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">M</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="c4">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43_1_1_1_2"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="ref" href="matrix_1.html#T23" title="MATRIX_1:th.23">MATRIX_1:23</a></span>;<br/><a NAME="E2:43_1_1_1_2_2"/>
(  <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"><span class="p3">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">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"><span class="p2">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">b1</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="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T23" title="MATRIX_1:th.23">MATRIX_1:23</a>, <a class="ref" href="matrlin.html#D7" title="MATRLIN:def.7">MATRLIN:def 7</a></span>;<br/><a NAME="E3:43_1_1_1_2_2"/><span class="kw">then </span>
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</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"><span class="p4">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c6">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E28">A24</font></span></a>, <a class="ref" href="matrix_3.html#D4" title="MATRIX_3:def.4">MATRIX_3:def 4</a></span>;<br/><a NAME="E4:43_1_1_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A25</font></span>: 
 <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"><span class="p5">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c6">M</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>;<br/><a NAME="E5:43_1_1_1_2_2"/><span class="lab"><font color="Green" title="E30">A26</font></span>: 
(  <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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">b1</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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T23" title="MATRIX_1:th.23">MATRIX_1:23</a>, <a class="ref" href="matrlin.html#D7" title="MATRLIN:def.7">MATRLIN:def 7</a></span>;<br/><a NAME="E6:43_1_1_1_2_2"/><span class="kw">then </span>
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c6">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E28">A24</font></span></a>, <a class="ref" href="matrix_3.html#D4" title="MATRIX_3:def.4">MATRIX_3:def 4</a></span>;<br/><a NAME="E7:43_1_1_1_2_2"/><span class="kw">then </span>
 <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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c6">M</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>;<br/><a NAME="E8:43_1_1_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A27</font></span>: 
 <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"><span class="p5">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E29">A25</font></span></a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></span>;<br/> <a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span> = 
 <a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="fvsum_1.html#K9" title="FVSUM_1:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T18" target="_self" title="MATRLIN2:th.18">Th18</a></span>
<br/>.= 
<font color="Maroon" title="c8">a</font> <a href="matrix13.html#K2" title="MATRIX13:func.2">*</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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix15.html#T29" title="MATRIX15:th.29">MATRIX15:29</a></span>
;<br/><a NAME="E10:43_1_1_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A28</font></span>: 
<span class="p1">(<span class="default"><a href="matrix15.html#K2" title="MATRIX15:func.2">LineVec2Mx</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">a</font> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E28">A24</font></span></a>, <a class="txt" href="#E5:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E30">A26</font></span></a>, <a class="ref" href="matrix15.html#T1" title="MATRIX15:th.1">MATRIX15:1</a></span>;<br/><a NAME="E11:43_1_1_1_2_2"/><span class="lab"><font color="Green" title="E33">A29</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</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="c5">B2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="matrlin2.html#E7"><span class="lab"><font color="Green" title="E4">Lm1</font></span></a></span>;<br/><a NAME="E12:43_1_1_1_2_2"/><span class="lab"><font color="Green" title="E34">A30</font></span>: 
<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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</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="c5">B2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="matrlin2.html#E7"><span class="lab"><font color="Green" title="E4">Lm1</font></span></a></span>;<br/><a NAME="E13:43_1_1_1_2_2"/>
 <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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T23" title="MATRIX_1:th.23">MATRIX_1:23</a></span>;<br/><a NAME="E14:43_1_1_1_2_2"/><span class="kw">then </span>
 <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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E28">A24</font></span></a>, <a class="txt" href="#E5:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E30">A26</font></span></a>, <a class="ref" href="matrix_3.html#D4" title="MATRIX_3:def.4">MATRIX_3:def 4</a></span>;<br/><a NAME="E15:43_1_1_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A31</font></span>: 
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</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"><span class="p4">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">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> (<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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E32">A28</font></span></a>, <a class="ref" href="matrixr1.html#T20" title="MATRIXR1:th.20">MATRIXR1:20</a></span>;<br/><div><span class="lab"><font color="Green" title="E36">A32</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1_1_2_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c16">i</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">i</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#K5" title="MATRLIN:func.5">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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> implies <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">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#K5" title="MATRLIN:func.5">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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">i</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:43_1_1_1_2_2_2"/><span class="lab"><font color="Green" title="E37">A33</font></span>: 
<font color="Maroon" title="c16">i</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#K5" title="MATRLIN:func.5">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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">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#K5" title="MATRLIN:func.5">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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">i</font></span>)</span></span><br/><a NAME="E2:43_1_1_1_2_2_2"/><span class="lab"><font color="Green" title="E38">A34</font></span>: 
<span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43_1_1_1_2_2_2"><span class="lab"><font color="Green" title="E37">A33</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/><a NAME="E3:43_1_1_1_2_2_2"/>
<font color="Maroon" title="c16">i</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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E34">A30</font></span></a>, <a class="txt" href="#E1:43_1_1_1_2_2_2"><span class="lab"><font color="Green" title="E37">A33</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><a NAME="E4:43_1_1_1_2_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A35</font></span>: 
<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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">i</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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/><a NAME="E5:43_1_1_1_2_2_2"/>
<font color="Maroon" title="c16">i</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="c5">B2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E34">A30</font></span></a>, <a class="txt" href="#E1:43_1_1_1_2_2_2"><span class="lab"><font color="Green" title="E37">A33</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><a NAME="E6:43_1_1_1_2_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A36</font></span>: 
<font color="Maroon" title="c5">B2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">B2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/><a NAME="E7:43_1_1_1_2_2_2"/><span class="lab"><font color="Green" title="E41">A37</font></span>: 
<font color="Maroon" title="c16">i</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"><span class="p5">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E31">A27</font></span></a>, <a class="txt" href="#E12:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E34">A30</font></span></a>, <a class="txt" href="#E1:43_1_1_1_2_2_2"><span class="lab"><font color="Green" title="E37">A33</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><a NAME="E8:43_1_1_1_2_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A38</font></span>: 
<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"><span class="p5">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">i</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"><span class="p5">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">i</font> = 
 the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">lmult</a> of <font color="Maroon" title="c3">V2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">B2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">i</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E33">A29</font></span></a>, <a class="txt" href="#E8:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E31">A27</font></span></a>, <a class="txt" href="#E12:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E34">A30</font></span></a>, <a class="txt" href="#E1:43_1_1_1_2_2_2"><span class="lab"><font color="Green" title="E37">A33</font></span></a>, <a class="txt" href="#E6:43_1_1_1_2_2_2"><span class="lab"><font color="Green" title="E40">A36</font></span></a>, <a class="ref" href="funcop_1.html#T22" title="FUNCOP_1:th.22">FUNCOP_1:22</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">i</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="c5">B2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E35">A31</font></span></a>, <a class="txt" href="#E7:43_1_1_1_2_2_2"><span class="lab"><font color="Green" title="E41">A37</font></span></a>, <a class="txt" href="#E4:43_1_1_1_2_2_2"><span class="lab"><font color="Green" title="E39">A35</font></span></a>, <a class="txt" href="#E8:43_1_1_1_2_2_2"><span class="lab"><font color="Green" title="E42">A38</font></span></a>, <a class="ref" href="fvsum_1.html#T50" title="FVSUM_1:th.50">FVSUM_1:50</a></span>
<br/>.= 
<font color="Maroon" title="c8">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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">i</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="c5">B2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">i</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D16" title="VECTSP_1:def.16">VECTSP_1:def 16</a></span>
<br/>.= 
<font color="Maroon" title="c8">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#K5" title="MATRLIN:func.5">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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c16">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43_1_1_1_2_2_2"><span class="lab"><font color="Green" title="E37">A33</font></span></a>, <a class="txt" href="#E4:43_1_1_1_2_2_2"><span class="lab"><font color="Green" title="E39">A35</font></span></a>, <a class="txt" href="#E6:43_1_1_1_2_2_2"><span class="lab"><font color="Green" title="E40">A36</font></span></a>, <a class="txt" href="#E2:43_1_1_1_2_2_2"><span class="lab"><font color="Green" title="E38">A34</font></span></a>, <a class="ref" href="funcop_1.html#T22" title="FUNCOP_1:th.22">FUNCOP_1:22</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E17:43_1_1_1_2_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">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#K5" title="MATRLIN:func.5">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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E33">A29</font></span></a>, <a class="txt" href="#E8:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E31">A27</font></span></a>, <a class="txt" href="#E12:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E34">A30</font></span></a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></span>;<br/><a NAME="E18:43_1_1_1_2_2"/><span class="kw">then </span>
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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"><span class="p0">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">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#K4" title="RLVECT_1:func.4">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:43_1_1_1_2_2"><span class="lab"><font color="Green" title="E36">A32</font></span></a>, <a class="ref" href="rlvect_2.html#T67" title="RLVECT_2:th.67">RLVECT_2:67</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> = 
<font color="Maroon" title="c8">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#K4" title="RLVECT_1:func.4">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">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="c9">v1</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c4">b1</font></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c6">M</font></span>)</span>,1)</span>)</span>,<font color="Maroon" title="c5">B2</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#D3" target="_self" title="MATRLIN2:def.3">Def3</a></span>
<br/>.= 
<font color="Maroon" title="c8">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#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">v1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#D3" target="_self" title="MATRLIN2:def.3">Def3</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E4:43_1_1_1_2"/><span class="kw">then </span>
(  <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>) is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  &amp;  <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>) is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43_1_1_1_2"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="grcat_1.html#D8" title="GRCAT_1:def.8">GRCAT_1:def 8</a>, <a class="ref" href="mod_2.html#D2" title="MOD_2:def.2">MOD_2:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E5:43_1_1_1_2"/>
(  <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>) is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  &amp;  <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">B2</font>) is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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