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

<span class="kw">let </span><font color="Maroon" title="c3">r</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_3.html#K5" title="ARYTM_3:func.5">RAT+</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_3.html#K5" title="ARYTM_3:func.5">RAT+</a>  st <font color="Maroon" title="c3">r</font> <a href="arytm_3.html#NR4" title="ARYTM_3:NR.4">&lt;</a> <font color="Olive" title="b1">s</font></span><br/>

<span class="kw">take </span><font color="Maroon" title="c4">s</font> = <font color="Maroon" title="c3">r</font> <a href="arytm_3.html#K9" title="ARYTM_3:func.9">+</a> <a href="arytm_3.html#K12" title="ARYTM_3:func.12">one</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">r</font> <a href="arytm_3.html#NR4" title="ARYTM_3:NR.4">&lt;</a> <font color="Maroon" title="c4">s</font></span><br/>

<a NAME="E1:107"/>
<font color="Maroon" title="c4">s</font> <a href="arytm_3.html#K9" title="ARYTM_3:func.9">+</a> <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_3.html#T50" target="_self" title="ARYTM_3:th.50">Th56</a></span>;<br/>
<a NAME="E2:107"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A1</font></span>: 
<font color="Maroon" title="c3">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_3.html#T62" target="_self" title="ARYTM_3:th.62">Th69</a></span>;<br/>
<a NAME="E3:107"/>
<font color="Maroon" title="c3">r</font> <a href="arytm_3.html#R3" title="ARYTM_3:pred.3">&lt;='</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_3.html#D13" target="_self" title="ARYTM_3:def.13">Def13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:107"/>
<font color="Maroon" title="c3">r</font> <a href="arytm_3.html#NR4" title="ARYTM_3:NR.4">&lt;</a> <font color="Maroon" title="c4">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:107"><span class="lab"><font color="Green" title="E80">A1</font></span></a>, <a class="ref" href="arytm_3.html#T66" target="_self" title="ARYTM_3:th.66">Th73</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
