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<span class="kw">let </span><font color="Maroon" title="c1">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">i</font>, <font color="Olive" title="b3">n</font>, <font color="Olive" title="b4">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><br/> for <font color="Olive" title="b5">A</font> being  <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <font color="Maroon" title="c1">D</font><br/> for <font color="Olive" title="b6">nt</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Olive" title="b3">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/> for <font color="Olive" title="b7">mt</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Olive" title="b1">m</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b2">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="Olive" title="b3">n</font> &amp; <font color="Olive" title="b4">j</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="Olive" title="b3">n</font> &amp; <font color="Olive" title="b6">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">j</font> holds <br/> <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Olive" title="b5">A</font>,<font color="Olive" title="b6">nt</font>,<font color="Olive" title="b7">mt</font></span>)</span>,<font color="Olive" title="b2">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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Olive" title="b5">A</font>,<font color="Olive" title="b6">nt</font>,<font color="Olive" title="b7">mt</font></span>)</span>,<font color="Olive" title="b4">j</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c3">i</font>, <font color="Maroon" title="c4">n</font>, <font color="Maroon" title="c5">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <font color="Maroon" title="c1">D</font><br/> for <font color="Olive" title="b2">nt</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c4">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/> for <font color="Olive" title="b3">mt</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c2">m</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c4">n</font> &amp; <font color="Maroon" title="c5">j</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="c4">n</font> &amp; <font color="Olive" title="b2">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font> holds <br/> <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">nt</font>,<font color="Olive" title="b3">mt</font></span>)</span>,<font color="Maroon" title="c3">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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">nt</font>,<font color="Olive" title="b3">mt</font></span>)</span>,<font color="Maroon" title="c5">j</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">A</font> be   <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <font color="Maroon" title="c1">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">nt</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c4">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/> for <font color="Olive" title="b2">mt</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c2">m</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c4">n</font> &amp; <font color="Maroon" title="c5">j</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="c4">n</font> &amp; <font color="Olive" title="b1">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font> holds <br/> <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Olive" title="b1">nt</font>,<font color="Olive" title="b2">mt</font></span>)</span>,<font color="Maroon" title="c3">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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Olive" title="b1">nt</font>,<font color="Olive" title="b2">mt</font></span>)</span>,<font color="Maroon" title="c5">j</font></span><br/><span class="kw">let </span><font color="Maroon" title="c7">nt</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c4">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">mt</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c2">m</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c4">n</font> &amp; <font color="Maroon" title="c5">j</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="c4">n</font> &amp; <font color="Maroon" title="c7">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font> holds <br/> <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Olive" title="b1">mt</font></span>)</span>,<font color="Maroon" title="c3">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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Olive" title="b1">mt</font></span>)</span>,<font color="Maroon" title="c5">j</font></span><br/><span class="kw">let </span><font color="Maroon" title="c8">mt</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c2">m</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c4">n</font> &amp; <font color="Maroon" title="c5">j</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="c4">n</font> &amp; <font color="Maroon" title="c7">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font> implies  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>,<font color="Maroon" title="c3">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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>,<font color="Maroon" title="c5">j</font> )</span><br/>















<span class="kw">set </span><font color="Maroon" title="c9">S</font> =  <a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">Li</font> =  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>,<font color="Maroon" title="c3">i</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">Lj</font> =  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>,<font color="Maroon" title="c5">j</font>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:26"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c4">n</font>
 <span class="kw">and </span><br/><a NAME="E2:26"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
<font color="Maroon" title="c5">j</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="c4">n</font>
 <span class="kw">and </span><br/><a NAME="E3:26"/><span class="lab"><font color="Green" title="E26">A3</font></span>: 
<font color="Maroon" title="c7">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>,<font color="Maroon" title="c3">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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>,<font color="Maroon" title="c5">j</font></span><br/>

<div><span class="lab"><font color="Green" title="E27">A4</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c12">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">k</font> &amp; <font color="Maroon" title="c12">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span> implies <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>,<font color="Maroon" title="c5">j</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">k</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:26_1"/><span class="lab"><font color="Green" title="E28">A5</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">k</font>
 <span class="kw">and </span><br/><a NAME="E2:26_1"/><span class="lab"><font color="Green" title="E29">A6</font></span>: 
<font color="Maroon" title="c12">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>,<font color="Maroon" title="c5">j</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">k</font></span><br/><a NAME="E3:26_1"/>
<font color="Maroon" title="c12">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></span>;<br/><a NAME="E4:26_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A7</font></span>: 
<font color="Maroon" title="c12">k</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="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26_1"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E2:26_1"><span class="lab"><font color="Green" title="E29">A6</font></span></a></span>;<br/><a NAME="E5:26_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c12">k</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c4">n</font></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p4">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E6:26_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c12">k</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T26" title="MATRIX_1:th.26">MATRIX_1:26</a></span>;<br/><a NAME="E7:26_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A8</font></span>: 
<span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">mt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix13.html#D1" target="_self" title="MATRIX13:def.1">Def1</a></span>;<br/><a NAME="E8:26_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">j</font>,<font color="Maroon" title="c12">k</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c4">n</font></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p4">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E4:26_1"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E9:26_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">j</font>,<font color="Maroon" title="c12">k</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T26" title="MATRIX_1:th.26">MATRIX_1:26</a></span>;<br/><a NAME="E10:26_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A9</font></span>: 
<span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">j</font>,<font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">nt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">mt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix13.html#D1" target="_self" title="MATRIX13:def.1">Def1</a></span>;<br/><a NAME="E11:26_1"/>
<span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:26_1"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></span>;<br/><span class="kw">hence </span><a NAME="E12:26_1"/>
<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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>,<font color="Maroon" title="c3">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>,<font color="Maroon" title="c5">j</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E4:26_1"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="txt" href="#E7:26_1"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="txt" href="#E10:26_1"><span class="lab"><font color="Green" title="E32">A9</font></span></a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E5:26"/><span class="lab"><font color="Green" title="E28">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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>,<font color="Maroon" title="c5">j</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> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></span>;<br/>
<a NAME="E6:26"/>
 <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>,<font color="Maroon" title="c3">i</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> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:26"/>
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>,<font color="Maroon" title="c3">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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">nt</font>,<font color="Maroon" title="c8">mt</font></span>)</span>,<font color="Maroon" title="c5">j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:26"><span class="lab"><font color="Green" title="E28">A10</font></span></a>, <a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
