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

<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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">  for <font color="Olive" title="b1">p</font> being   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</a>  st  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 holds <br/><font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</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="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 implies <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">pn</font> = <font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">x</font> = <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font>;<br/>
<span class="kw">assume </span><a NAME="E1:97"/><span class="lab"><font color="Green" title="E39">A1</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ; <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"> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span><br/>

<a NAME="E2:97"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A2</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E3:97"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A3</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T54" target="_self" onmouseover="rs('afinsq_1/T54')" onmouseout="rh()">Th51</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E42">A4</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="97_1"><span class="kw">now </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">  for <font color="Olive" title="b1">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c2">p</font> holds <br/><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">m</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">m</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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"> ( <font color="Maroon" title="c5">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c2">p</font> implies <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> )</span><br/><span class="kw">assume </span><a NAME="E1:97_1"/>
<font color="Maroon" title="c5">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c2">p</font>
 ; <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"> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font></span><br/><a NAME="E2:97_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="afinsq_1.html#E9"><span class="lab"><font color="Green" title="E4">Lm1</font></span></a></span>;<br/><a NAME="E3:97_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A5</font></span>: 
<font color="Maroon" title="c5">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E39">A1</font></span></a>, <a class="txt" href="#E3:97"><span class="lab"><font color="Green" title="E41">A3</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="97_1_1"><span class="kw">now </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"> ( ( <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> ) or ( <font color="Maroon" title="c5">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> ) )</span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:97_1_1_1"/>
( <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> or <font color="Maroon" title="c5">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_1"><span class="kw">case </span></a><a NAME="E1:97_1_1_1_1"/>
<font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</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"> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:97_1_1_1_1"/>
<font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97"><span class="lab"><font color="Green" title="E41">A3</font></span></a>, <a class="ref" href="afinsq_1.html#T36" target="_self" onmouseover="rs('afinsq_1/T36')" onmouseout="rh()">Th33</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><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_2"><span class="kw">case </span></a><a NAME="E1:97_1_1_1_2"/>
<font color="Maroon" title="c5">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</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"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font></span><br/><div class="add"><a NAME="E2:97_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97_1"><span class="lab"><font color="Green" title="E43">A5</font></span></a>, <a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</a></span>;<br/><a NAME="E3:97_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A6</font></span>: 
<font color="Maroon" title="c5">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="afinsq_1.html#E9"><span class="lab"><font color="Green" title="E4">Lm1</font></span></a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#D3" target="_self" onmouseover="rs('afinsq_1/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
<font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:97"><span class="lab"><font color="Green" title="E40">A2</font></span></a>, <a class="txt" href="#E3:97"><span class="lab"><font color="Green" title="E41">A3</font></span></a>, <a class="txt" href="#E3:97_1_1_1_2"><span class="lab"><font color="Green" title="E44">A6</font></span></a>, <a class="ref" href="afinsq_1.html#T53" target="_self" onmouseover="rs('afinsq_1/T53')" onmouseout="rh()">Th50</a></span>
;<br/> <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><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:97_1"/>
<font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font>
 ; <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><span class="kw">end;</span></div>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> = 
<font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97"><span class="lab"><font color="Green" title="E41">A3</font></span></a>, <a class="ref" href="afinsq_1.html#D3" target="_self" onmouseover="rs('afinsq_1/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E39">A1</font></span></a>, <a class="ref" href="afinsq_1.html#D4" target="_self" onmouseover="rs('afinsq_1/D4')" onmouseout="rh()">Def4</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E6:97"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:97"><span class="lab"><font color="Green" title="E42">A4</font></span></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>
