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<span class="kw">let </span><font color="Maroon" title="c3">l</font>, <font color="Maroon" title="c4">j</font>, <font color="Maroon" title="c5">i</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies ( <font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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> iff <font color="Maroon" title="c5">i</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> <font color="Maroon" title="c4">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c6">k</font> ) )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:57"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
<font color="Maroon" title="c4">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">and </span><br/><a NAME="E2:57"/><span class="lab"><font color="Green" title="E54">A2</font></span>: 
<font color="Maroon" title="c3">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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> iff <font color="Maroon" title="c5">i</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> <font color="Maroon" title="c4">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c6">k</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c7">x</font> = <font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">j</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">y</font> = <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>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">ny</font> =  <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>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">dy</font> =  <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>;<br/>
<a NAME="E3:57"/><span class="lab"><font color="Green" title="E55">A3</font></span>: 
 <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>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="ref" href="arytm_3.html#T42" target="_self" title="ARYTM_3:th.42">Th48</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">nx</font> =  <a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">j</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">dx</font> =  <a href="arytm_3.html#K7" title="ARYTM_3:func.7">denominator</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">j</font></span>)</span>;<br/>
<a NAME="E4:57"/><span class="lab"><font color="Green" title="E56">A4</font></span>: 
 <a href="arytm_3.html#K7" title="ARYTM_3:func.7">denominator</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">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">j</font>,<font color="Maroon" title="c5">i</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="arytm_3.html#T42" target="_self" title="ARYTM_3:th.42">Th48</a></span>;<br/>
<a NAME="E5:57"/><span class="lab"><font color="Green" title="E57">A5</font></span>: 
 <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>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="ref" href="arytm_3.html#T42" target="_self" title="ARYTM_3:th.42">Th48</a></span>;<br/>
<a NAME="E6:57"/><span class="lab"><font color="Green" title="E58">A6</font></span>: 
 <a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">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">i</font>,<font color="Maroon" title="c4">j</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="arytm_3.html#T42" target="_self" title="ARYTM_3:th.42">Th48</a></span>;<br/>
<div><span class="kw">hereby </span> <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="c5">i</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> <font color="Maroon" title="c4">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c6">k</font> implies <font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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>
<div class="add"><span class="kw">assume </span><a NAME="E1:57_1"/>
<font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">i</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> <font color="Maroon" title="c4">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c6">k</font></span><br/><a NAME="E2:57_1"/><span class="kw">then </span>
( <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <span class="p2">(<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>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">hcf</a> <font color="Maroon" title="c4">j</font></span>)</span> &amp; <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="arytm_3.html#K7" title="ARYTM_3:func.7">denominator</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">j</font></span>)</span></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p1">(<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E6:57"><span class="lab"><font color="Green" title="E58">A6</font></span></a>, <a class="txt" href="#E5:57"><span class="lab"><font color="Green" title="E57">A5</font></span></a>, <a class="ref" href="arytm_3.html#T21" target="_self" title="ARYTM_3:th.21">Th26</a></span>;<br/><span class="kw">hence </span><font color="Maroon" title="c5">i</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c3">l</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <span class="p4">(<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>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">hcf</a> <font color="Maroon" title="c4">j</font></span>)</span></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p2">(<span class="default"><a href="arytm_3.html#K7" title="ARYTM_3:func.7">denominator</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">j</font></span>)</span></span>)</span></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p1">(<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 class="kw">by</span> <span class="lab"><a class="ref" href="ordinal3.html#T50" title="ORDINAL3:th.50">ORDINAL3:50</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <span class="p3">(<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>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K3" title="ARYTM_3:func.3">hcf</a> <font color="Maroon" title="c4">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#K7" title="ARYTM_3:func.7">denominator</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">j</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p1">(<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 class="kw">by</span> <span class="lab"><a class="ref" href="ordinal3.html#T50" title="ORDINAL3:th.50">ORDINAL3:50</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <span class="p3">(<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>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c4">j</font></span>)</span> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p1">(<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E4:57"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="ref" href="arytm_3.html#T21" target="_self" title="ARYTM_3:th.21">Th26</a></span>
<br/>.= 
<font color="Maroon" title="c4">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <span class="p3">(<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>)</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal3.html#T50" title="ORDINAL3:th.50">ORDINAL3:50</a></span>
<br/>.= 
<font color="Maroon" title="c4">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c6">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:57"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="ref" href="arytm_3.html#T21" target="_self" title="ARYTM_3:th.21">Th26</a></span>
;<br/> <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>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E8:57"/><span class="lab"><font color="Green" title="E59">A7</font></span>: 
<font color="Maroon" title="c5">i</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> <font color="Maroon" title="c4">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c6">k</font>
 ; <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="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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><br/>

<a NAME="E9:57"/><span class="kw">then </span>
 <a href="arytm_3.html#K7" title="ARYTM_3:func.7">denominator</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">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> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c3">l</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c6">k</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="txt" href="#E4:57"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="ref" href="arytm_3.html#T28" target="_self" title="ARYTM_3:th.28">Th33</a></span>;<br/>
<a NAME="E10:57"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A8</font></span>: 
 <a href="arytm_3.html#K7" title="ARYTM_3:func.7">denominator</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E5:57"><span class="lab"><font color="Green" title="E57">A5</font></span></a>, <a class="ref" href="arytm_3.html#T28" target="_self" title="ARYTM_3:th.28">Th33</a></span>;<br/>
<a NAME="E11:57"/>
 <a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">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> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c6">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">j</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c3">l</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="txt" href="#E6:57"><span class="lab"><font color="Green" title="E58">A6</font></span></a>, <a class="txt" href="#E8:57"><span class="lab"><font color="Green" title="E59">A7</font></span></a>, <a class="ref" href="arytm_3.html#T28" target="_self" title="ARYTM_3:th.28">Th33</a></span>;<br/>
<a NAME="E12:57"/><span class="kw">then </span>
 <a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E3:57"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="ref" href="arytm_3.html#T28" target="_self" title="ARYTM_3:th.28">Th33</a></span>;<br/>
<a NAME="E13:57"/><span class="kw">then </span>
<font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="arytm_3.html#K6" title="ARYTM_3:func.6">numerator</a> <span class="p2">(<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>)</span> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <span class="p1">(<span class="default"><a href="arytm_3.html#K7" title="ARYTM_3:func.7">denominator</a> <span class="p2">(<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>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:57"><span class="lab"><font color="Green" title="E60">A8</font></span></a>, <a class="ref" href="arytm_3.html#T39" target="_self" title="ARYTM_3:th.39">Th45</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:57"/>
<font color="Maroon" title="c5">i</font> <a href="arytm_3.html#K8" title="ARYTM_3:func.8">/</a> <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 class="kw">by</span> <span class="lab"><a class="ref" href="arytm_3.html#T39" target="_self" title="ARYTM_3:th.39">Th45</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/>


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