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<b>reconsider </b><font color="Maroon" title="c7">A'</font> =  <a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c6">b2</font> as   <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c6">b2</font></span>)</span>, <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c6">b2</font></span>)</span>,<font color="Maroon" title="c1">K</font> <b>by </b><i><a class="ref" href="matrix_2.html#T7" title="MATRIX_2:th.7">MATRIX_2:7</a></i>;<br/>
<a NAME="E2:31_1_1"/><i><font color="Green" title="E18">A1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">A'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">B1</font>
 
<b>by </b><i><a class="ref" href="matrlin.html#D10" title="MATRLIN:def.10">MATRLIN:def 10</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_1_1_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">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="c5">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="31_1_1_1_1"><b>suppose </b></a><a NAME="E1:31_1_1_1_1"/><i><font color="Green" title="E19">A2</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c6">b2</font> is   <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">B1</font>, <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">b2</font>,<font color="Maroon" title="c1">K</font></span><br/><div class="add"><a NAME="E2:31_1_1_1_1"/><b>then </b>
 <a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c6">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="matrlin2.html#E2:31_1_1"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="card_2.html#T59" title="CARD_2:th.59">CARD_2:59</a></i>;<br/><b>hence </b><a NAME="E3:31_1_1_1_1"/>
 <a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c6">b2</font> is   <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">B1</font>, <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">b2</font>,<font color="Maroon" title="c1">K</font>
 <b>by </b><i><a class="txt" href="matrlin2.html#E1:31_1_1_1_1"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="matrix_1.html#T13" title="MATRIX_1:th.13">MATRIX_1:13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1_2"><b>suppose </b></a><a NAME="E1:31_1_1_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c6">b2</font> is   <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">B1</font>, <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">b2</font>,<font color="Maroon" title="c1">K</font></span><br/><div class="add"><a NAME="E2:31_1_1_1_2"/><b>then </b><i><font color="Green" title="E19">A3</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">B1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">B1</font></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">B1</font></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">A'</font> )
 <b>by </b><i><a class="txt" href="matrlin2.html#E2:31_1_1"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="finseq_1.html#T5" title="FINSEQ_1:th.5">FINSEQ_1:5</a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/><b>then </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">B1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">B1</font></span>)</span></span>)</span></span>)</span> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c6">b2</font> = 
<font color="Maroon" title="c7">A'</font> <a href="matrlin.html#K1" title="MATRLIN:func.1">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">B1</font></span>)</span>
<b>by </b><i><a class="ref" href="matrlin.html#D10" title="MATRLIN:def.10">MATRLIN:def 10</a></i>
<br/>.= 
<font color="Maroon" title="c7">A'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">B1</font></span>)</span>
<b>by </b><i><a class="txt" href="matrlin2.html#E2:31_1_1_1_2"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
<br/>.= 
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c7">A'</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">B1</font></span>)</span>
<b>by </b><i><a class="txt" href="matrlin2.html#E2:31_1_1"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="matrlin2.html#E2:31_1_1_1_2"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="matrix_2.html#T10" title="MATRIX_2:th.10">MATRIX_2:10</a></i>
;<br/><b>then </b> <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c7">A'</font> = 
 <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="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">B1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">B1</font></span>)</span></span>)</span></span>)</span> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c6">b2</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">b2</font>
<b>by </b><i><a class="ref" href="matrlin.html#D9" title="MATRLIN:def.9">MATRLIN:def 9</a></i>
;<br/><b>hence </b><a NAME="E5:31_1_1_1_2"/>
 <a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">B1</font>,<font color="Maroon" title="c6">b2</font> is   <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">B1</font>, <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">b2</font>,<font color="Maroon" title="c1">K</font>
 <b>by </b><i><a class="ref" href="matrlin.html#D10" title="MATRLIN:def.10">MATRLIN:def 10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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