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<div class="add">

<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">n</font>, <font color="Maroon" title="c3">l</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">D</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">M</font> being   <a href="matrix_1.html#M1" title="MATRIX_1:mode.1">Matrix</a> of <font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">m</font>,<font color="Olive" title="b1">D</font><br/> for <font color="Olive" title="b3">pD</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Olive" title="b1">D</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">pD</font> <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="Olive" title="b2">M</font> holds <br/>for <font color="Olive" title="b4">p'</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Olive" title="b1">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>   st <font color="Olive" title="b3">pD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">p'</font> holds <br/> <a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Olive" title="b2">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Olive" title="b3">pD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Olive" title="b2">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Olive" title="b4">p'</font></span><br/><b>let </b><font color="Maroon" title="c4">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">M</font> being   <a href="matrix_1.html#M1" title="MATRIX_1:mode.1">Matrix</a> of <font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c4">D</font><br/> for <font color="Olive" title="b2">pD</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c4">D</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">pD</font> <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="Olive" title="b1">M</font> holds <br/>for <font color="Olive" title="b3">p'</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c4">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>   st <font color="Olive" title="b2">pD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">p'</font> holds <br/> <a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Olive" title="b1">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Olive" title="b2">pD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Olive" title="b1">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Olive" title="b3">p'</font></span><br/><b>let </b><font color="Maroon" title="c5">M</font> be    <a href="matrix_1.html#M1" title="MATRIX_1:mode.1">Matrix</a> of <font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c4">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">pD</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c4">D</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">pD</font> <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="c5">M</font> holds <br/>for <font color="Olive" title="b2">p'</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c4">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>   st <font color="Olive" title="b1">pD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">p'</font> holds <br/> <a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Olive" title="b1">pD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Olive" title="b2">p'</font></span><br/><b>let </b><font color="Maroon" title="c6">pD</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c4">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">pD</font> <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="c5">M</font> implies for <font color="Olive" title="b1">p'</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c4">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>   st <font color="Maroon" title="c6">pD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p'</font> holds <br/> <a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Olive" title="b1">p'</font> )</span><br/>











<b>assume </b><a NAME="E1:42"/><i><font color="Green" title="E35">A1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">pD</font> <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="c5">M</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p'</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c4">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>   st <font color="Maroon" title="c6">pD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p'</font> holds <br/> <a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Olive" title="b1">p'</font></span><br/>

<b>let </b><font color="Maroon" title="c7">p'</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c4">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">pD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">p'</font> implies  <a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font> )</span><br/>

<b>assume </b><a NAME="E2:42"/><i><font color="Green" title="E36">A2</font></i>: 
<font color="Maroon" title="c6">pD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">p'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span><br/>

<b>set </b><font color="Maroon" title="c8">RL</font> =  <a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font>;<br/>
<b>set </b><font color="Maroon" title="c9">R</font> =  <a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font>;<br/>
<a NAME="E3:42"/><i><font color="Green" title="E37">A3</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">M</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">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> <span class="p1">(<span class="default"><a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="matrix11.html#E34"><i><font color="Green" title="E33">Lm4</font></i></a>, <a class="ref" href="finseq_7.html#T7" title="FINSEQ_7:th.7">FINSEQ_7:7</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">i</font> &amp; <font color="Maroon" title="c10">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span> implies <span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font> )</span><br/><b>assume </b><a NAME="E1:42_1"/><i><font color="Green" title="E38">A4</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">i</font> &amp; <font color="Maroon" title="c10">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font></span><br/><a NAME="E2:42_1"/>
<font color="Maroon" title="c10">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/><a NAME="E3:42_1"/><b>then </b>
<font color="Maroon" title="c10">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="matrix11.html#E1:42_1"><i><font color="Green" title="E38">A4</font></i></a></i>;<br/><a NAME="E4:42_1"/><b>then </b><i><font color="Green" title="E39">A5</font></i>: 
( <font color="Maroon" title="c10">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="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span> &amp; <font color="Maroon" title="c10">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">M</font> &amp; <font color="Maroon" title="c10">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font> &amp; <font color="Maroon" title="c2">n</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">M</font> )
 <b>by </b><i><a class="txt" href="matrix11.html#E3:42"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a>, <a class="ref" href="matrix_1.html#D3" title="MATRIX_1:def.3">MATRIX_1:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:42_1_1_1"/>
( <font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">l</font> or <font color="Maroon" title="c10">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">l</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1_1"><b>case </b></a><a NAME="E1:42_1_1_1_1"/>
<font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">l</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font></span><br/><div class="add"><a NAME="E2:42_1_1_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">p'</font> &amp; <span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font> &amp;  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font></span>)</span>,<font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">pD</font> &amp;  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font></span>)</span>,<font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font> )
 <b>by </b><i><a class="txt" href="matrix11.html#E1:42"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="matrix11.html#E3:42"><i><font color="Green" title="E37">A3</font></i></a>, <a class="txt" href="matrix11.html#E1:42_1"><i><font color="Green" title="E38">A4</font></i></a>, <a class="txt" href="matrix11.html#E4:42_1"><i><font color="Green" title="E39">A5</font></i></a>, <a class="ref" href="matrix11.html#T28" target="_self" title="MATRIX11:th.28">Th28</a>, <a class="ref" href="finseq_7.html#T10" title="FINSEQ_7:th.10">FINSEQ_7:10</a>, <a class="ref" href="matrix_2.html#T10" title="MATRIX_2:th.10">MATRIX_2:10</a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>;<br/><b>hence </b><a NAME="E3:42_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font>
 <b>by </b><i><a class="txt" href="matrix11.html#E2:42"><i><font color="Green" title="E36">A2</font></i></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="42_1_1_1_2"><b>case </b></a><a NAME="E1:42_1_1_1_2"/>
<font color="Maroon" title="c10">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">l</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font></span><br/><div class="add"><a NAME="E2:42_1_1_1_2"/><b>then </b>
( <span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font> &amp; <span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font> &amp; <font color="Maroon" title="c5">M</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font> &amp; <font color="Maroon" title="c5">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c10">i</font> &amp;  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font></span>)</span>,<font color="Maroon" title="c10">i</font> &amp;  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font></span>)</span>,<font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font> )
 <b>by </b><i><a class="txt" href="matrix11.html#E3:42"><i><font color="Green" title="E37">A3</font></i></a>, <a class="txt" href="matrix11.html#E1:42_1"><i><font color="Green" title="E38">A4</font></i></a>, <a class="txt" href="matrix11.html#E4:42_1"><i><font color="Green" title="E39">A5</font></i></a>, <a class="ref" href="matrix11.html#T28" target="_self" title="MATRIX11:th.28">Th28</a>, <a class="ref" href="finseq_7.html#T12" title="FINSEQ_7:th.12">FINSEQ_7:12</a>, <a class="ref" href="matrix_2.html#T10" title="MATRIX_2:th.10">MATRIX_2:10</a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>;<br/><b>hence </b><a NAME="E3:42_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font>
 ; <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></div><b>end;</b></div><b>hence </b><a NAME="E6:42_1"/>
<span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:42"/>
 <a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">pD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> <font color="Maroon" title="c5">M</font>,<font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c7">p'</font>
 <b>by </b><i><a class="txt" href="matrix11.html#E3:42"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
