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

<b>let </b><font color="Maroon" title="c3">l</font>, <font color="Maroon" title="c4">i</font>, <font color="Maroon" title="c5">j</font>, <font color="Maroon" title="c6">k</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a> <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <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"><font color="Maroon" title="c4">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c5">j</font></span>)</span> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c3">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c3">l</font></span>)</span></span><br/>







<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:64_1"/>
( ( <font color="Maroon" title="c5">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  &amp; <font color="Maroon" title="c3">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  ) or <font color="Maroon" title="c5">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  or <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1_1"><b>suppose </b></a><a NAME="E1:64_1_1"/><i><font color="Green" title="E58">A1</font></i>: 
( <font color="Maroon" title="c5">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  &amp; <font color="Maroon" title="c3">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  )
 ; <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"><font color="Maroon" title="c4">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c5">j</font></span>)</span> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c3">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c3">l</font></span>)</span></span><br/><div class="add"><a NAME="E2:64_1_1"/><b>then </b>
(  <a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c3">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c6">k</font>,<font color="Maroon" title="c3">l</font> &amp;  <a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c5">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font> &amp;  <a href="arytm_3.html#K7" title="ARYTM_3:func.7">denominator</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c3">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">k</font> &amp;  <a href="arytm_3.html#K7" title="ARYTM_3:func.7">denominator</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c5">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c5">j</font>,<font color="Maroon" title="c4">i</font> )
 <b>by </b><i><a class="ref" href="arytm_3.html#T48" target="_self" title="ARYTM_3:th.48">Th48</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c5">j</font></span>)</span> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c3">l</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p3">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c6">k</font>,<font color="Maroon" title="c3">l</font></span>)</span></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">hcf</a> <font color="Maroon" title="c5">j</font></span>)</span></span>)</span> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c5">j</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p3">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">k</font></span>)</span></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">hcf</a> <font color="Maroon" title="c5">j</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="arytm_3.html#E1:64_1_1"><i><font color="Green" title="E58">A1</font></i></a>, <a class="ref" href="arytm_3.html#T20" target="_self" title="ARYTM_3:th.20">Th20</a>, <a class="ref" href="arytm_3.html#T50" target="_self" title="ARYTM_3:th.50">Th50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c6">k</font>,<font color="Maroon" title="c3">l</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">hcf</a> <font color="Maroon" title="c5">j</font></span>)</span></span>)</span></span>)</span> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c5">j</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p3">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">k</font></span>)</span></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">hcf</a> <font color="Maroon" title="c5">j</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ordinal3.html#T58" title="ORDINAL3:th.58">ORDINAL3:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c6">k</font>,<font color="Maroon" title="c3">l</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c5">j</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p3">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">k</font></span>)</span></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">hcf</a> <font color="Maroon" title="c5">j</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="arytm_3.html#T26" target="_self" title="ARYTM_3:th.26">Th26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c6">k</font>,<font color="Maroon" title="c3">l</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">k</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c5">j</font>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">hcf</a> <font color="Maroon" title="c5">j</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ordinal3.html#T58" title="ORDINAL3:th.58">ORDINAL3:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c6">k</font>,<font color="Maroon" title="c3">l</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">k</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c5">j</font></span>)</span>
<b>by </b><i><a class="ref" href="arytm_3.html#T26" target="_self" title="ARYTM_3:th.26">Th26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c6">k</font>,<font color="Maroon" title="c3">l</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">l</font> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">hcf</a> <font color="Maroon" title="c6">k</font></span>)</span></span>)</span> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">k</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c5">j</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">l</font> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">hcf</a> <font color="Maroon" title="c6">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="arytm_3.html#E1:64_1_1"><i><font color="Green" title="E58">A1</font></i></a>, <a class="ref" href="arytm_3.html#T20" target="_self" title="ARYTM_3:th.20">Th20</a>, <a class="ref" href="arytm_3.html#T50" target="_self" title="ARYTM_3:th.50">Th50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c6">k</font>,<font color="Maroon" title="c3">l</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">l</font> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">hcf</a> <font color="Maroon" title="c6">k</font></span>)</span></span>)</span></span>)</span> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">k</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c5">j</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">l</font> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">hcf</a> <font color="Maroon" title="c6">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ordinal3.html#T58" title="ORDINAL3:th.58">ORDINAL3:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">k</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c5">j</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">l</font> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">hcf</a> <font color="Maroon" title="c6">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="arytm_3.html#T26" target="_self" title="ARYTM_3:th.26">Th26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="arytm_3.html#K4" title="ARYTM_3:func.4">RED</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c6">k</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">l</font> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">hcf</a> <font color="Maroon" title="c6">k</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ordinal3.html#T58" title="ORDINAL3:th.58">ORDINAL3:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c3">l</font></span>)</span>
<b>by </b><i><a class="ref" href="arytm_3.html#T26" target="_self" title="ARYTM_3:th.26">Th26</a></i>
;<br/> <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="64_1_2"><b>suppose </b></a><a NAME="E1:64_1_2"/>
( <font color="Maroon" title="c5">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  or <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  )
 ; <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"><font color="Maroon" title="c4">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c5">j</font></span>)</span> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c3">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c3">l</font></span>)</span></span><br/><div class="add"><a NAME="E2:64_1_2"/><b>then </b>
( ( <font color="Maroon" title="c4">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c5">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  or <font color="Maroon" title="c6">k</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  ) &amp; <font color="Maroon" title="c5">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  )
 <b>by </b><i><a class="ref" href="arytm_3.html#D10" target="_self" title="ARYTM_3:def.10">Def10</a>, <a class="ref" href="ordinal2.html#T52" title="ORDINAL2:th.52">ORDINAL2:52</a></i>;<br/><a NAME="E3:64_1_2"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c5">j</font></span>)</span> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c3">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c3">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  )
 <b>by </b><i><a class="ref" href="arytm_3.html#D10" target="_self" title="ARYTM_3:def.10">Def10</a>, <a class="ref" href="arytm_3.html#T54" target="_self" title="ARYTM_3:th.54">Th54</a></i>;<br/><b>hence </b><a NAME="E4:64_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c5">j</font></span>)</span> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c3">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c3">l</font></span>)</span>
 ; <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>
