<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E19">Def06</font></span>   defines <a href="music_s1.html#K9" title="MUSIC_S1:func.9">EQUIV_RAT_ratio</a> <a onclick="hs(this)" href="javascript:()">MUSIC_S1:def 10 : <br/></a><span> for <font color="Olive">b<sub>1</sub></font> being   <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="music_s1.html#K1" title="MUSIC_S1:func.1">RATPLUS</a>,<a href="music_s1.html#K1" title="MUSIC_S1:func.1">RATPLUS</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="music_s1.html#K1" title="MUSIC_S1:func.1">RATPLUS</a>,<a href="music_s1.html#K1" title="MUSIC_S1:func.1">RATPLUS</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> holds <br/> ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="music_s1.html#K9" title="MUSIC_S1:func.9">EQUIV_RAT_ratio</a>  iff  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="music_s1.html#K1" title="MUSIC_S1:func.1">RATPLUS</a>,<a href="music_s1.html#K1" title="MUSIC_S1:func.1">RATPLUS</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> holds <br/> ( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive">b<sub>1</sub></font> iff  ex <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</font>, <font color="Olive" title="b6">c</font>, <font color="Olive" title="b7">d</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="music_s1.html#K1" title="MUSIC_S1:func.1">RATPLUS</a>  st <br/>( <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> &amp; <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b6">c</font>,<font color="Olive" title="b7">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> &amp;  <a href="music_s1.html#K7" title="MUSIC_S1:func.7">RAT_ratio</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="music_s1.html#K7" title="MUSIC_S1:func.7">RAT_ratio</a> (<font color="Olive" title="b6">c</font>,<font color="Olive" title="b7">d</font>) ) ) );<br/></span></div>
