<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">x1</font>, <font color="Maroon" title="c2">x2</font>, <font color="Maroon" title="c3">y1</font>, <font color="Maroon" title="c4">y2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>) <a href="matrix_0.html#K12" title="MATRIX_0:func.12">][</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>) <a href="matrix_0.html#K12" title="MATRIX_0:func.12">][</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>) <a href="matrix_0.html#K12" title="MATRIX_0:func.12">][</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2</span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">M</font> = (<font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>) <a href="matrix_0.html#K12" title="MATRIX_0:func.12">][</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>);<br/>
<span class="kw">thus </span><a NAME="E1:70"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>) <a href="matrix_0.html#K12" title="MATRIX_0:func.12">][</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" onmouseover="rs('finseq_1/T44')" onmouseout="rh()">FINSEQ_1:44</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>) <a href="matrix_0.html#K12" title="MATRIX_0:func.12">][</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>) <a href="matrix_0.html#K12" title="MATRIX_0:func.12">][</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2</span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )</span><br/>

<a NAME="E2:70"/>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>) <a href="matrix_0.html#K12" title="MATRIX_0:func.12">][</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T127" onmouseover="rs('finseq_2/T127')" onmouseout="rh()">FINSEQ_2:127</a></span>;<br/>
<a NAME="E3:70"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A2</font></span>: 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>) <a href="matrix_0.html#K12" title="MATRIX_0:func.12">][</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/>
<a NAME="E4:70"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" onmouseover="rs('finseq_1/T44')" onmouseout="rh()">FINSEQ_1:44</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:70"/>
 <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>) <a href="matrix_0.html#K12" title="MATRIX_0:func.12">][</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="txt" href="#E3:70"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="ref" href="matrix_0.html#D3" target="_self" onmouseover="rs('matrix_0/D3')" onmouseout="rh()">Def3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>) <a href="matrix_0.html#K12" title="MATRIX_0:func.12">][</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2</span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span><br/>

<span class="kw">hence </span><a NAME="E6:70"/>
 <a href="matrix_0.html#K2" title="MATRIX_0:func.2">Indices</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>) <a href="matrix_0.html#K12" title="MATRIX_0:func.12">][</a> (<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c4">y2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2</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="#E1:70"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="finseq_1.html#D3" onmouseover="rs('finseq_1/D3')" onmouseout="rh()">FINSEQ_1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
