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<span class="kw">let </span><font color="Maroon" title="c1">i1</font>, <font color="Maroon" title="c2">j1</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="arytm_3.html#NK9" title="ARYTM_3:NK.9">quotient</a> (<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">j1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">j1</font></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">x</font> =  <a href="arytm_3.html#NK9" title="ARYTM_3:NK.9">quotient</a> (<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">j1</font>);<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:1_1"/>
( <font color="Maroon" title="c2">j1</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="c2">j1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_1_1"><span class="kw">suppose </span></a><a NAME="E1:1_1_1"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
<font color="Maroon" title="c2">j1</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="arytm_3.html#NK9" title="ARYTM_3:NK.9">quotient</a> (<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">j1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">j1</font></span><br/><div class="add"><span class="kw">hence </span> <a href="arytm_3.html#NK9" title="ARYTM_3:NK.9">quotient</a> (<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">j1</font>) = 
 <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_3.html#D10" title="ARYTM_3:def.10">ARYTM_3:def 10</a></span>
<br/>.= 
<font color="Maroon" title="c1">i1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">j1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:1_1_1"><span class="lab"><font color="Green" title="E3">A1</font></span></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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_1_2"><span class="kw">suppose </span></a><a NAME="E1:1_1_2"/><span class="lab"><font color="Green" title="E3">A2</font></span>: 
<font color="Maroon" title="c2">j1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="arytm_3.html#NK9" title="ARYTM_3:NK.9">quotient</a> (<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">j1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">j1</font></span><br/><div class="add"><a NAME="E2:1_1_2"/>
 <a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<span class="p1">(<span class="default"><a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_0.html#D3" title="ARYTM_0:def.3">ARYTM_0:def 3</a></span>;<br/><a NAME="E3:1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E4">A3</font></span>: 
 <a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_0.html#T11" title="ARYTM_0:th.11">ARYTM_0:11</a></span>;<br/><a NAME="E4:1_1_2"/>
<font color="Maroon" title="c2">j1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">j1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:1_1_2"><span class="lab"><font color="Green" title="E3">A2</font></span></a>, <a class="ref" href="xcmplx_0.html#D7" title="XCMPLX_0:def.7">XCMPLX_0:def 7</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">x1</font>, <font color="Maroon" title="c5">x2</font>, <font color="Maroon" title="c6">y1</font>, <font color="Maroon" title="c7">y2</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E6:1_1_2"/><span class="lab"><font color="Green" title="E5">A4</font></span>: 
<font color="Maroon" title="c2">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c5">x2</font></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
 <span class="kw">and </span><br/><a NAME="E7:1_1_2"/><span class="lab"><font color="Green" title="E6">A5</font></span>: 
<font color="Maroon" title="c2">j1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c6">y1</font>,<font color="Maroon" title="c7">y2</font></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
 <span class="kw">and </span><br/><a NAME="E8:1_1_2"/><span class="lab"><font color="Green" title="E7">A6</font></span>: 
1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><span class="p2">(<span class="default"><a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> (<span class="p3">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c6">y1</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <span class="p4">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c7">y2</font>)</span>)</span></span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> (<span class="p3">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c7">y2</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y1</font>)</span>)</span>)</span>)</span></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_0.html#D5" title="XCMPLX_0:def.5">XCMPLX_0:def 5</a></span>;<br/><a NAME="E9:1_1_2"/>
 <a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> (<span class="p1">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c7">y2</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y1</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:1_1_2"><span class="lab"><font color="Green" title="E7">A6</font></span></a>, <a class="ref" href="arytm_0.html#T24" title="ARYTM_0:th.24">ARYTM_0:24</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E8">A7</font></span>: 1 = 
 <a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> (<span class="p1">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c6">y1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <span class="p2">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c7">y2</font>)</span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:1_1_2"><span class="lab"><font color="Green" title="E7">A6</font></span></a>, <a class="ref" href="arytm_0.html#D5" title="ARYTM_0:def.5">ARYTM_0:def 5</a></span>
<br/>.= 
 <a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> (<span class="p1">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c6">y1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:1_1_2"><span class="lab"><font color="Green" title="E5">A4</font></span></a>, <a class="ref" href="arytm_0.html#T12" title="ARYTM_0:th.12">ARYTM_0:12</a>, <a class="ref" href="arytm_0.html#T24" title="ARYTM_0:th.24">ARYTM_0:24</a></span>
<br/>.= 
 <a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c6">y1</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:1_1_2"><span class="lab"><font color="Green" title="E4">A3</font></span></a>, <a class="ref" href="arytm_0.html#T11" title="ARYTM_0:th.11">ARYTM_0:11</a></span>
;<br/><a NAME="E11:1_1_2"/>
<font color="Maroon" title="c5">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:1_1_2"><span class="lab"><font color="Green" title="E5">A4</font></span></a>, <a class="ref" href="arytm_0.html#T24" title="ARYTM_0:th.24">ARYTM_0:24</a></span>;<br/><a NAME="E12:1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">A8</font></span>: 
<font color="Maroon" title="c2">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:1_1_2"><span class="lab"><font color="Green" title="E5">A4</font></span></a>, <a class="ref" href="arytm_0.html#D5" title="ARYTM_0:def.5">ARYTM_0:def 5</a></span>;<br/><a NAME="E13:1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> 
 ;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">xx</font> = <font color="Maroon" title="c4">x1</font> as    <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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="rat_1.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c9">yy</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> <span class="kw"> such that </span><br/><a NAME="E16:1_1_2"/><span class="lab"><font color="Green" title="E10">A9</font></span>: 
<font color="Maroon" title="c8">xx</font> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <font color="Maroon" title="c9">yy</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K12" title="ARYTM_3:func.12">one</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:1_1_2"><span class="lab"><font color="Green" title="E3">A2</font></span></a>, <a class="txt" href="#E12:1_1_2"><span class="lab"><font color="Green" title="E9">A8</font></span></a>, <a class="ref" href="arytm_3.html#T54" title="ARYTM_3:th.54">ARYTM_3:54</a></span>;<br/><a NAME="E17:1_1_2"/><span class="lab"><font color="Green" title="E11">A10</font></span>: 
<font color="Maroon" title="c8">xx</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="arytm_3.html#K5" title="ARYTM_3:func.5">RAT+</a> 
 ;<br/><a NAME="E18:1_1_2"/>
<font color="Maroon" title="c9">yy</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="arytm_3.html#K5" title="ARYTM_3:func.5">RAT+</a> 
 ;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">xx1</font> = <font color="Maroon" title="c8">xx</font>, <font color="Maroon" title="c11">yy1</font> = <font color="Maroon" title="c9">yy</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_2.html#K2" title="ARYTM_2:func.2">REAL+</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:1_1_2"><span class="lab"><font color="Green" title="E11">A10</font></span></a>, <a class="ref" href="arytm_2.html#T1" title="ARYTM_2:th.1">ARYTM_2:1</a></span>;<br/><a NAME="E20:1_1_2"/><span class="lab"><font color="Green" title="E12">A11</font></span>: 
 ex <font color="Olive" title="b1">x9</font>, <font color="Olive" title="b2">y9</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 <br/>( <font color="Maroon" title="c10">xx1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x9</font> &amp; <font color="Maroon" title="c11">yy1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y9</font> &amp; <font color="Maroon" title="c10">xx1</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c11">yy1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x9</font> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <font color="Olive" title="b2">y9</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_2.html#T21" title="ARYTM_2:th.21">ARYTM_2:21</a></span>;<br/><a NAME="E21:1_1_2"/>
<font color="Maroon" title="c11">yy1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="arytm_2.html#K2" title="ARYTM_2:func.2">REAL+</a> 
 ;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">xx1</font> = <font color="Maroon" title="c10">xx1</font>, <font color="Maroon" title="c13">yy1</font> = <font color="Maroon" title="c11">yy1</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_0.html#T1" title="ARYTM_0:th.1">ARYTM_0:1</a></span>;<br/><a NAME="E23:1_1_2"/>
 ex <font color="Olive" title="b1">x9</font>, <font color="Olive" title="b2">y9</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_2.html#K2" title="ARYTM_2:func.2">REAL+</a>  st <br/>( <font color="Maroon" title="c12">xx1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x9</font> &amp; <font color="Maroon" title="c13">yy1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y9</font> &amp;  <a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c12">xx1</font>,<font color="Maroon" title="c13">yy1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x9</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Olive" title="b2">y9</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_0.html#D2" title="ARYTM_0:def.2">ARYTM_0:def 2</a></span>;<br/><a NAME="E24:1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A12</font></span>: 
<font color="Maroon" title="c9">yy</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:1_1_2"><span class="lab"><font color="Green" title="E3">A2</font></span></a>, <a class="txt" href="#E12:1_1_2"><span class="lab"><font color="Green" title="E9">A8</font></span></a>, <a class="txt" href="#E10:1_1_2"><span class="lab"><font color="Green" title="E8">A7</font></span></a>, <a class="txt" href="#E16:1_1_2"><span class="lab"><font color="Green" title="E10">A9</font></span></a>, <a class="txt" href="#E20:1_1_2"><span class="lab"><font color="Green" title="E12">A11</font></span></a>, <a class="ref" href="arytm_0.html#T18" title="ARYTM_0:th.18">ARYTM_0:18</a></span>;<br/><a NAME="E25:1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A13</font></span>: 
<font color="Maroon" title="c6">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="arytm_3.html#K5" title="ARYTM_3:func.5">RAT+</a> 
 ;<br/><a NAME="E26:1_1_2"/>
<font color="Maroon" title="c7">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:1_1_2"><span class="lab"><font color="Green" title="E6">A5</font></span></a>, <a class="ref" href="arytm_0.html#T24" title="ARYTM_0:th.24">ARYTM_0:24</a></span>;<br/><a NAME="E27:1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A14</font></span>: 
<font color="Maroon" title="c2">j1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:1_1_2"><span class="lab"><font color="Green" title="E6">A5</font></span></a>, <a class="ref" href="arytm_0.html#D5" title="ARYTM_0:def.5">ARYTM_0:def 5</a></span>;<br/><a NAME="E28:1_1_2"/><span class="lab"><font color="Green" title="E16">A15</font></span>: 
<font color="Maroon" title="c2">j1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> 
 ;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c14">a</font> =  <a href="arytm_3.html#NK9" title="ARYTM_3:NK.9">quotient</a> (<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">j1</font>), <font color="Maroon" title="c15">b</font> = <font color="Maroon" title="c2">j1</font> as    <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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="rat_1.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c16">x91</font>, <font color="Maroon" title="c17">x92</font>, <font color="Maroon" title="c18">y91</font>, <font color="Maroon" title="c19">y92</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E31:1_1_2"/><span class="lab"><font color="Green" title="E17">A16</font></span>: 
<font color="Maroon" title="c1">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c16">x91</font>,<font color="Maroon" title="c17">x92</font></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
 <span class="kw">and </span><br/><a NAME="E32:1_1_2"/><span class="lab"><font color="Green" title="E18">A17</font></span>: 
<font color="Maroon" title="c2">j1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c18">y91</font>,<font color="Maroon" title="c19">y92</font></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
 <span class="kw">and </span><br/><a NAME="E33:1_1_2"/><span class="lab"><font color="Green" title="E19">A18</font></span>: 
<font color="Maroon" title="c1">i1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">j1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><span class="p2">(<span class="default"><a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> (<span class="p3">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c16">x91</font>,<font color="Maroon" title="c18">y91</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <span class="p4">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c17">x92</font>,<font color="Maroon" title="c19">y92</font>)</span>)</span></span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> (<span class="p3">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c16">x91</font>,<font color="Maroon" title="c19">y92</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c17">x92</font>,<font color="Maroon" title="c18">y91</font>)</span>)</span>)</span>)</span></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_0.html#D5" title="XCMPLX_0:def.5">XCMPLX_0:def 5</a></span>;<br/><a NAME="E34:1_1_2"/><span class="lab"><font color="Green" title="E20">A19</font></span>: 
 <a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> (<span class="p1">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c16">x91</font>,<font color="Maroon" title="c19">y92</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c17">x92</font>,<font color="Maroon" title="c18">y91</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:1_1_2"><span class="lab"><font color="Green" title="E19">A18</font></span></a>, <a class="ref" href="arytm_0.html#T24" title="ARYTM_0:th.24">ARYTM_0:24</a></span>;<br/><a NAME="E35:1_1_2"/>
<font color="Maroon" title="c4">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:1_1_2"><span class="lab"><font color="Green" title="E9">A8</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c20">x19</font>, <font color="Maroon" title="c21">y19</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_2.html#K2" title="ARYTM_2:func.2">REAL+</a> <span class="kw"> such that </span><br/><a NAME="E37:1_1_2"/><span class="lab"><font color="Green" title="E21">A20</font></span>: 
<font color="Maroon" title="c4">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">x19</font>
 <span class="kw">and </span><br/><a NAME="E38:1_1_2"/><span class="lab"><font color="Green" title="E22">A21</font></span>: 
<font color="Maroon" title="c6">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">y19</font>
 <span class="kw">and </span><br/><a NAME="E39:1_1_2"/><span class="lab"><font color="Green" title="E23">A22</font></span>: 
 <a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c6">y1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">x19</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c21">y19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:1_1_2"><span class="lab"><font color="Green" title="E14">A13</font></span></a>, <a class="ref" href="arytm_0.html#D2" title="ARYTM_0:def.2">ARYTM_0:def 2</a>, <a class="ref" href="arytm_2.html#T1" title="ARYTM_2:th.1">ARYTM_2:1</a>, <a class="ref" href="arytm_2.html#T2" title="ARYTM_2:th.2">ARYTM_2:2</a></span>;<br/><a NAME="E40:1_1_2"/><span class="lab"><font color="Green" title="E24">A23</font></span>: 
 ex <font color="Olive" title="b1">x199</font>, <font color="Olive" title="b2">y199</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 <br/>( <font color="Maroon" title="c20">x19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x199</font> &amp; <font color="Maroon" title="c21">y19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y199</font> &amp; <font color="Maroon" title="c20">x19</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c21">y19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x199</font> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <font color="Olive" title="b2">y199</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:1_1_2"><span class="lab"><font color="Green" title="E9">A8</font></span></a>, <a class="txt" href="#E24:1_1_2"><span class="lab"><font color="Green" title="E13">A12</font></span></a>, <a class="txt" href="#E28:1_1_2"><span class="lab"><font color="Green" title="E16">A15</font></span></a>, <a class="txt" href="#E37:1_1_2"><span class="lab"><font color="Green" title="E21">A20</font></span></a>, <a class="txt" href="#E38:1_1_2"><span class="lab"><font color="Green" title="E22">A21</font></span></a>, <a class="txt" href="rat_1.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a>, <a class="ref" href="arytm_2.html#T21" title="ARYTM_2:th.21">ARYTM_2:21</a></span>;<br/><a NAME="E41:1_1_2"/><span class="lab"><font color="Green" title="E25">A24</font></span>: 
<font color="Maroon" title="c19">y92</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:1_1_2"><span class="lab"><font color="Green" title="E18">A17</font></span></a>, <a class="ref" href="arytm_0.html#T24" title="ARYTM_0:th.24">ARYTM_0:24</a></span>;<br/><a NAME="E42:1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">j1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">y91</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:1_1_2"><span class="lab"><font color="Green" title="E18">A17</font></span></a>, <a class="ref" href="arytm_0.html#D5" title="ARYTM_0:def.5">ARYTM_0:def 5</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A25</font></span>: <font color="Maroon" title="c1">i1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">j1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a></span>)</span> = 
 <a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> (<span class="p1">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c16">x91</font>,<font color="Maroon" title="c6">y1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="arytm_0.html#K3" title="ARYTM_0:func.3">opp</a> <span class="p2">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c17">x92</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:1_1_2"><span class="lab"><font color="Green" title="E15">A14</font></span></a>, <a class="txt" href="#E33:1_1_2"><span class="lab"><font color="Green" title="E19">A18</font></span></a>, <a class="txt" href="#E41:1_1_2"><span class="lab"><font color="Green" title="E25">A24</font></span></a>, <a class="txt" href="#E34:1_1_2"><span class="lab"><font color="Green" title="E20">A19</font></span></a>, <a class="ref" href="arytm_0.html#D5" title="ARYTM_0:def.5">ARYTM_0:def 5</a></span>
<br/>.= 
 <a href="arytm_0.html#K1" title="ARYTM_0:func.1">+</a> (<span class="p1">(<span class="default"><a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c16">x91</font>,<font color="Maroon" title="c6">y1</font>)</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:1_1_2"><span class="lab"><font color="Green" title="E4">A3</font></span></a>, <a class="ref" href="arytm_0.html#T12" title="ARYTM_0:th.12">ARYTM_0:12</a></span>
<br/>.= 
 <a href="arytm_0.html#K2" title="ARYTM_0:func.2">*</a> (<font color="Maroon" title="c16">x91</font>,<font color="Maroon" title="c6">y1</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_0.html#T11" title="ARYTM_0:th.11">ARYTM_0:11</a></span>
;<br/><a NAME="E44:1_1_2"/>
<font color="Maroon" title="c17">x92</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:1_1_2"><span class="lab"><font color="Green" title="E17">A16</font></span></a>, <a class="ref" href="arytm_0.html#T24" title="ARYTM_0:th.24">ARYTM_0:24</a></span>;<br/><a NAME="E45:1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A26</font></span>: 
<font color="Maroon" title="c1">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">x91</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:1_1_2"><span class="lab"><font color="Green" title="E17">A16</font></span></a>, <a class="ref" href="arytm_0.html#D5" title="ARYTM_0:def.5">ARYTM_0:def 5</a></span>;<br/><a NAME="E46:1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A27</font></span>: 
<font color="Maroon" title="c16">x91</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> 
 ;<br/><a NAME="E47:1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c16">x91</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="arytm_3.html#K5" title="ARYTM_3:func.5">RAT+</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="rat_1.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c22">x9</font>, <font color="Maroon" title="c23">y9</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_2.html#K2" title="ARYTM_2:func.2">REAL+</a> <span class="kw"> such that </span><br/><a NAME="E49:1_1_2"/><span class="lab"><font color="Green" title="E29">A28</font></span>: 
<font color="Maroon" title="c16">x91</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">x9</font>
 <span class="kw">and </span><br/><a NAME="E50:1_1_2"/><span class="lab"><font color="Green" title="E30">A29</font></span>: 
<font color="Maroon" title="c6">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">y9</font>
 <span class="kw">and </span><br/><a NAME="E51:1_1_2"/><span class="lab"><font color="Green" title="E31">A30</font></span>: 
<font color="Maroon" title="c1">i1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">j1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">x9</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c23">y9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:1_1_2"><span class="lab"><font color="Green" title="E26">A25</font></span></a>, <a class="txt" href="#E25:1_1_2"><span class="lab"><font color="Green" title="E14">A13</font></span></a>, <a class="ref" href="arytm_0.html#D2" title="ARYTM_0:def.2">ARYTM_0:def 2</a>, <a class="ref" href="arytm_2.html#T1" title="ARYTM_2:th.1">ARYTM_2:1</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c24">x99</font>, <font color="Maroon" title="c25">y99</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> <span class="kw"> such that </span><br/><a NAME="E53:1_1_2"/><span class="lab"><font color="Green" title="E32">A31</font></span>: 
<font color="Maroon" title="c22">x9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">x99</font>
 <span class="kw">and </span><br/><a NAME="E54:1_1_2"/><span class="lab"><font color="Green" title="E33">A32</font></span>: 
<font color="Maroon" title="c23">y9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">y99</font>
 <span class="kw">and </span><br/><a NAME="E55:1_1_2"/><span class="lab"><font color="Green" title="E34">A33</font></span>: 
<font color="Maroon" title="c1">i1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">j1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">x99</font> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <font color="Maroon" title="c25">y99</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E46:1_1_2"><span class="lab"><font color="Green" title="E28">A27</font></span></a>, <a class="txt" href="#E24:1_1_2"><span class="lab"><font color="Green" title="E13">A12</font></span></a>, <a class="txt" href="#E49:1_1_2"><span class="lab"><font color="Green" title="E29">A28</font></span></a>, <a class="txt" href="#E50:1_1_2"><span class="lab"><font color="Green" title="E30">A29</font></span></a>, <a class="txt" href="#E51:1_1_2"><span class="lab"><font color="Green" title="E31">A30</font></span></a>, <a class="txt" href="rat_1.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a>, <a class="ref" href="arytm_2.html#T21" title="ARYTM_2:th.21">ARYTM_2:21</a></span>;<br/><font color="Maroon" title="c14">a</font> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <font color="Maroon" title="c15">b</font> = 
<span class="p1">(<span class="default"><a href="arytm_3.html#NK9" title="ARYTM_3:NK.9">quotient</a> (<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">j1</font>)</span>)</span> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <span class="p1">(<span class="default"><a href="arytm_3.html#NK9" title="ARYTM_3:NK.9">quotient</a> (<font color="Maroon" title="c2">j1</font>,<a href="arytm_3.html#K12" title="ARYTM_3:func.12">one</a>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_3.html#T40" title="ARYTM_3:th.40">ARYTM_3:40</a></span>
<br/>.= 
 <a href="arytm_3.html#NK9" title="ARYTM_3:NK.9">quotient</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">i1</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <font color="Maroon" title="c2">j1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">j1</font> <a href="ordinal3.html#K9" title="ORDINAL3:func.9">*^</a> <a href="arytm_3.html#K12" title="ARYTM_3:func.12">one</a></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_3.html#T49" title="ARYTM_3:th.49">ARYTM_3:49</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="arytm_3.html#NK9" title="ARYTM_3:NK.9">quotient</a> (<font color="Maroon" title="c1">i1</font>,<a href="arytm_3.html#K12" title="ARYTM_3:func.12">one</a>)</span>)</span> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <span class="p1">(<span class="default"><a href="arytm_3.html#NK9" title="ARYTM_3:NK.9">quotient</a> (<font color="Maroon" title="c2">j1</font>,<font color="Maroon" title="c2">j1</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_3.html#T49" title="ARYTM_3:th.49">ARYTM_3:49</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="arytm_3.html#NK9" title="ARYTM_3:NK.9">quotient</a> (<font color="Maroon" title="c1">i1</font>,<a href="arytm_3.html#K12" title="ARYTM_3:func.12">one</a>)</span>)</span> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <a href="arytm_3.html#K12" title="ARYTM_3:func.12">one</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:1_1_2"><span class="lab"><font color="Green" title="E3">A2</font></span></a>, <a class="ref" href="arytm_3.html#T41" title="ARYTM_3:th.41">ARYTM_3:41</a></span>
<br/>.= 
 <a href="arytm_3.html#NK9" title="ARYTM_3:NK.9">quotient</a> (<font color="Maroon" title="c1">i1</font>,<a href="arytm_3.html#K12" title="ARYTM_3:func.12">one</a>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_3.html#T53" title="ARYTM_3:th.53">ARYTM_3:53</a></span>
<br/>.= 
<font color="Maroon" title="c1">i1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_3.html#T40" title="ARYTM_3:th.40">ARYTM_3:40</a></span>
<br/>.= 
<font color="Maroon" title="c24">x99</font> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <a href="arytm_3.html#K12" title="ARYTM_3:func.12">one</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E45:1_1_2"><span class="lab"><font color="Green" title="E27">A26</font></span></a>, <a class="txt" href="#E49:1_1_2"><span class="lab"><font color="Green" title="E29">A28</font></span></a>, <a class="txt" href="#E53:1_1_2"><span class="lab"><font color="Green" title="E32">A31</font></span></a>, <a class="ref" href="arytm_3.html#T53" title="ARYTM_3:th.53">ARYTM_3:53</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c24">x99</font> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <font color="Maroon" title="c25">y99</font></span>)</span> <a href="arytm_3.html#K10" title="ARYTM_3:func.10">*'</a> <font color="Maroon" title="c15">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:1_1_2"><span class="lab"><font color="Green" title="E9">A8</font></span></a>, <a class="txt" href="#E10:1_1_2"><span class="lab"><font color="Green" title="E8">A7</font></span></a>, <a class="txt" href="#E50:1_1_2"><span class="lab"><font color="Green" title="E30">A29</font></span></a>, <a class="txt" href="#E54:1_1_2"><span class="lab"><font color="Green" title="E33">A32</font></span></a>, <a class="txt" href="#E37:1_1_2"><span class="lab"><font color="Green" title="E21">A20</font></span></a>, <a class="txt" href="#E38:1_1_2"><span class="lab"><font color="Green" title="E22">A21</font></span></a>, <a class="txt" href="#E39:1_1_2"><span class="lab"><font color="Green" title="E23">A22</font></span></a>, <a class="txt" href="#E40:1_1_2"><span class="lab"><font color="Green" title="E24">A23</font></span></a>, <a class="ref" href="arytm_3.html#T52" title="ARYTM_3:th.52">ARYTM_3:52</a></span>
;<br/><span class="kw">hence </span><a NAME="E57:1_1_2"/>
 <a href="arytm_3.html#NK9" title="ARYTM_3:NK.9">quotient</a> (<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">j1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">j1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:1_1_2"><span class="lab"><font color="Green" title="E3">A2</font></span></a>, <a class="txt" href="#E55:1_1_2"><span class="lab"><font color="Green" title="E34">A33</font></span></a>, <a class="ref" href="arytm_3.html#T56" title="ARYTM_3:th.56">ARYTM_3:56</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><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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