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<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="gcd_1.html#NM3" title="GCD_1:NM.3">gcdDomain</a>;<br/><b>let </b><font color="Maroon" title="c2">Amp</font> be    <a href="gcd_1.html#M2" title="GCD_1:mode.2">AmpleSet</a> of <font color="Maroon" title="c1">R</font>;<br/><b>let </b><font color="Maroon" title="c3">r1</font>, <font color="Maroon" title="c4">r2</font>, <font color="Maroon" title="c5">s1</font>, <font color="Maroon" title="c6">s2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>;<br/>





<b>assume </b><a NAME="E1:82"/><i><font color="Green" title="E60">A1</font></i>: 
( <font color="Maroon" title="c2">Amp</font> is <a href="gcd_1.html#V2" title="GCD_1:attr.2">multiplicative</a> &amp; <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#R8" title="GCD_1:pred.8">are_normalized_wrt</a> <font color="Maroon" title="c2">Amp</font> &amp; <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#R8" title="GCD_1:pred.8">are_normalized_wrt</a> <font color="Maroon" title="c2">Amp</font> )
 ;<br/>

<a NAME="E2:82"/><b>then </b>
(  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> &amp;  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c6">s2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Amp</font> &amp; <font color="Maroon" title="c4">r2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Amp</font> )
 
<b>by </b><i><a class="ref" href="gcd_1.html#D15" target="_self" title="GCD_1:def.15">Def15</a></i>;<br/>
<a NAME="E3:82"/><b>then </b><i><font color="Green" title="E61">A2</font></i>: 
( <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#R7" title="GCD_1:pred.7">are_co-prime</a>  &amp; <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#R7" title="GCD_1:pred.7">are_co-prime</a>  &amp; <font color="Maroon" title="c4">r2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c6">s2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c4">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gcd_1.html#K4" title="GCD_1:func.4">NF</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font> &amp; <font color="Maroon" title="c6">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gcd_1.html#K4" title="GCD_1:func.4">NF</a> <font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> )
 
<b>by </b><i><a class="txt" href="gcd_1.html#E1:82"><i><font color="Green" title="E60">A1</font></i></a>, <a class="ref" href="gcd_1.html#D9" target="_self" title="GCD_1:def.9">Def9</a>, <a class="ref" href="gcd_1.html#D14" target="_self" title="GCD_1:def.14">Def14</a>, <a class="ref" href="gcd_1.html#D15" target="_self" title="GCD_1:def.15">Def15</a></i>;<br/>
<a NAME="E4:82"/><b>then </b><i><font color="Green" title="E62">A3</font></i>: 
(  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> &amp;  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> )
 
<b>by </b><i><a class="ref" href="gcd_1.html#T34" target="_self" title="GCD_1:th.34">Th34</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="82_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:82_1_1"/>
( <font color="Maroon" title="c3">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> or <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> or ( <font color="Maroon" title="c4">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c6">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> ) or ( <font color="Maroon" title="c6">s2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c4">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> ) or ( <font color="Maroon" title="c4">r2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c6">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> ) or ( not <font color="Maroon" title="c3">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> &amp; not <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> &amp; (  not <font color="Maroon" title="c4">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> or  not <font color="Maroon" title="c6">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> ) &amp; (  not <font color="Maroon" title="c6">s2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> or  not <font color="Maroon" title="c4">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> ) &amp; (  not <font color="Maroon" title="c4">r2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> or  not <font color="Maroon" title="c6">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> ) ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1_1"><b>case </b></a><a NAME="E1:82_1_1_1"/><i><font color="Green" title="E63">A4</font></i>: 
( <font color="Maroon" title="c3">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> or <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> )
 ;<br/><div class="add"><a NAME="E2:82_1_1_1"/><b>then </b><i><font color="Green" title="E64">A5</font></i>: 
 <a href="gcd_1.html#K8" title="GCD_1:func.8">mult1</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D18" target="_self" title="GCD_1:def.18">Def18</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="82_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:82_1_1_1_1_1"/>
( <font color="Maroon" title="c3">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> or <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> )
 </span><b>by </b><i><a class="txt" href="gcd_1.html#E1:82_1_1_1"><i><font color="Green" title="E63">A4</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1_1_1_1_1"><b>case </b></a><a NAME="E1:82_1_1_1_1_1_1"/>
<font color="Maroon" title="c3">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font>
 ;<br/><div class="add"><b>then </b><span class="p1">(<span class="default"><a href="gcd_1.html#K9" title="GCD_1:func.9">mult2</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="gcd_1.html#K9" title="GCD_1:func.9">mult2</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font>
<b>by </b><i><a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></i>
;<br/><b>hence </b><a NAME="E3:82_1_1_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="gcd_1.html#K8" title="GCD_1:func.8">mult1</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K9" title="GCD_1:func.9">mult2</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span>
 <b>by </b><i><a class="txt" href="gcd_1.html#E2:82_1_1_1"><i><font color="Green" title="E64">A5</font></i></a>, <a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1_1_1_1_2"><b>case </b></a><a NAME="E1:82_1_1_1_1_1_2"/>
<font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font>
 ;<br/><div class="add"><b>then </b><span class="p1">(<span class="default"><a href="gcd_1.html#K9" title="GCD_1:func.9">mult2</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="gcd_1.html#K9" title="GCD_1:func.9">mult2</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font>
<b>by </b><i><a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></i>
;<br/><b>hence </b><a NAME="E3:82_1_1_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="gcd_1.html#K8" title="GCD_1:func.8">mult1</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K9" title="GCD_1:func.9">mult2</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span>
 <b>by </b><i><a class="txt" href="gcd_1.html#E2:82_1_1_1"><i><font color="Green" title="E64">A5</font></i></a>, <a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:82_1_1_1"/>
<span class="p1">(<span class="default"><a href="gcd_1.html#K8" title="GCD_1:func.8">mult1</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K9" title="GCD_1:func.9">mult2</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1_2"><b>case </b></a><a NAME="E1:82_1_1_2"/><i><font color="Green" title="E63">A6</font></i>: 
( <font color="Maroon" title="c4">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c6">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> )
 ;<br/><div class="add"><a NAME="E2:82_1_1_2"/><b>then </b><i><font color="Green" title="E64">A7</font></i>: 
 <a href="gcd_1.html#K8" title="GCD_1:func.8">mult1</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D18" target="_self" title="GCD_1:def.18">Def18</a></i>;<br/><a NAME="E3:82_1_1_2"/>
 <a href="gcd_1.html#K9" title="GCD_1:func.9">mult2</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="txt" href="gcd_1.html#E3:82"><i><font color="Green" title="E61">A2</font></i></a>, <a class="txt" href="gcd_1.html#E1:82_1_1_2"><i><font color="Green" title="E63">A6</font></i></a>, <a class="ref" href="gcd_1.html#D19" target="_self" title="GCD_1:def.19">Def19</a></i>;<br/><b>hence </b><a NAME="E4:82_1_1_2"/>
<span class="p1">(<span class="default"><a href="gcd_1.html#K8" title="GCD_1:func.8">mult1</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K9" title="GCD_1:func.9">mult2</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span>
 <b>by </b><i><a class="txt" href="gcd_1.html#E1:82_1_1_2"><i><font color="Green" title="E63">A6</font></i></a>, <a class="txt" href="gcd_1.html#E2:82_1_1_2"><i><font color="Green" title="E64">A7</font></i></a>, <a class="ref" href="vectsp_1.html#D13" title="VECTSP_1:def.13">VECTSP_1:def 13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1_3"><b>case </b></a><a NAME="E1:82_1_1_3"/><i><font color="Green" title="E63">A8</font></i>: 
( <font color="Maroon" title="c6">s2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c4">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> )
 ;<br/><div class="add"><a NAME="E2:82_1_1_3"/><b>then </b><i><font color="Green" title="E64">A9</font></i>: 
 <a href="gcd_1.html#K9" title="GCD_1:func.9">mult2</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>
 <b>by </b><i><a class="txt" href="gcd_1.html#E3:82"><i><font color="Green" title="E61">A2</font></i></a>, <a class="ref" href="gcd_1.html#D19" target="_self" title="GCD_1:def.19">Def19</a></i>;<br/><a NAME="E3:82_1_1_3"/>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c3">r1</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/><a NAME="E4:82_1_1_3"/><b>then </b><i><font color="Green" title="E65">A10</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#T7" target="_self" title="GCD_1:th.7">Th7</a></i>;<br/><a NAME="E5:82_1_1_3"/><b>then </b><i><font color="Green" title="E66">A11</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#T7" target="_self" title="GCD_1:th.7">Th7</a></i>;<br/><i><font color="Green" title="E67">A12</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font>
<b>by </b><i><a class="txt" href="gcd_1.html#E1:82_1_1_3"><i><font color="Green" title="E63">A8</font></i></a>, <a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>
<b>by </b><i><a class="txt" href="gcd_1.html#E4:82"><i><font color="Green" title="E62">A3</font></i></a>, <a class="txt" href="gcd_1.html#E4:82_1_1_3"><i><font color="Green" title="E65">A10</font></i></a>, <a class="txt" href="gcd_1.html#E5:82_1_1_3"><i><font color="Green" title="E66">A11</font></i></a>, <a class="ref" href="gcd_1.html#T11" target="_self" title="GCD_1:th.11">Th11</a></i>
;<br/><a NAME="E7:82_1_1_3"/><i><font color="Green" title="E68">A13</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c6">s2</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/><a NAME="E8:82_1_1_3"/><b>then </b><i><font color="Green" title="E69">A14</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c6">s2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">r1</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#T7" target="_self" title="GCD_1:th.7">Th7</a></i>;<br/><a NAME="E9:82_1_1_3"/><b>then </b><i><font color="Green" title="E70">A15</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">r1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#T7" target="_self" title="GCD_1:th.7">Th7</a></i>;<br/><span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">r1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">r1</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font>
<b>by </b><i><a class="txt" href="gcd_1.html#E4:82"><i><font color="Green" title="E62">A3</font></i></a>, <a class="txt" href="gcd_1.html#E7:82_1_1_3"><i><font color="Green" title="E68">A13</font></i></a>, <a class="txt" href="gcd_1.html#E8:82_1_1_3"><i><font color="Green" title="E69">A14</font></i></a>, <a class="ref" href="gcd_1.html#T11" target="_self" title="GCD_1:th.11">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">r1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>
<b>by </b><i><a class="txt" href="gcd_1.html#E4:82"><i><font color="Green" title="E62">A3</font></i></a>, <a class="txt" href="gcd_1.html#E8:82_1_1_3"><i><font color="Green" title="E69">A14</font></i></a>, <a class="txt" href="gcd_1.html#E9:82_1_1_3"><i><font color="Green" title="E70">A15</font></i></a>, <a class="ref" href="gcd_1.html#T11" target="_self" title="GCD_1:th.11">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
;<br/><b>hence </b><a NAME="E11:82_1_1_3"/>
<span class="p1">(<span class="default"><a href="gcd_1.html#K8" title="GCD_1:func.8">mult1</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K9" title="GCD_1:func.9">mult2</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span>
 <b>by </b><i><a class="txt" href="gcd_1.html#E1:82_1_1_3"><i><font color="Green" title="E63">A8</font></i></a>, <a class="txt" href="gcd_1.html#E2:82_1_1_3"><i><font color="Green" title="E64">A9</font></i></a>, <a class="txt" href="gcd_1.html#E6:82_1_1_3"><i><font color="Green" title="E67">A12</font></i></a>, <a class="ref" href="gcd_1.html#D18" target="_self" title="GCD_1:def.18">Def18</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1_4"><b>case </b></a><a NAME="E1:82_1_1_4"/><i><font color="Green" title="E63">A16</font></i>: 
( <font color="Maroon" title="c4">r2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c6">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> )
 ;<br/><div class="add"><a NAME="E2:82_1_1_4"/><b>then </b><i><font color="Green" title="E64">A17</font></i>: 
 <a href="gcd_1.html#K9" title="GCD_1:func.9">mult2</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>
 <b>by </b><i><a class="txt" href="gcd_1.html#E3:82"><i><font color="Green" title="E61">A2</font></i></a>, <a class="ref" href="gcd_1.html#D19" target="_self" title="GCD_1:def.19">Def19</a></i>;<br/><a NAME="E3:82_1_1_4"/>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c5">s1</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/><a NAME="E4:82_1_1_4"/><b>then </b><i><font color="Green" title="E65">A18</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c5">s1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">r1</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#T7" target="_self" title="GCD_1:th.7">Th7</a></i>;<br/><a NAME="E5:82_1_1_4"/><b>then </b><i><font color="Green" title="E66">A19</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">r1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">r2</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#T7" target="_self" title="GCD_1:th.7">Th7</a></i>;<br/><i><font color="Green" title="E67">A20</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">r2</font>
<b>by </b><i><a class="txt" href="gcd_1.html#E1:82_1_1_4"><i><font color="Green" title="E63">A16</font></i></a>, <a class="ref" href="vectsp_1.html#D13" title="VECTSP_1:def.13">VECTSP_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">r2</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>
<b>by </b><i><a class="txt" href="gcd_1.html#E4:82"><i><font color="Green" title="E62">A3</font></i></a>, <a class="txt" href="gcd_1.html#E4:82_1_1_4"><i><font color="Green" title="E65">A18</font></i></a>, <a class="txt" href="gcd_1.html#E5:82_1_1_4"><i><font color="Green" title="E66">A19</font></i></a>, <a class="ref" href="gcd_1.html#T11" target="_self" title="GCD_1:th.11">Th11</a></i>
;<br/><a NAME="E7:82_1_1_4"/><i><font color="Green" title="E68">A21</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c4">r2</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/><a NAME="E8:82_1_1_4"/><b>then </b><i><font color="Green" title="E69">A22</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">r1</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#T7" target="_self" title="GCD_1:th.7">Th7</a></i>;<br/><a NAME="E9:82_1_1_4"/><b>then </b><i><font color="Green" title="E70">A23</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">r1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#T7" target="_self" title="GCD_1:th.7">Th7</a></i>;<br/><span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">r1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">r1</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font>
<b>by </b><i><a class="txt" href="gcd_1.html#E4:82"><i><font color="Green" title="E62">A3</font></i></a>, <a class="txt" href="gcd_1.html#E7:82_1_1_4"><i><font color="Green" title="E68">A21</font></i></a>, <a class="txt" href="gcd_1.html#E8:82_1_1_4"><i><font color="Green" title="E69">A22</font></i></a>, <a class="ref" href="gcd_1.html#T11" target="_self" title="GCD_1:th.11">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">r1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>
<b>by </b><i><a class="txt" href="gcd_1.html#E4:82"><i><font color="Green" title="E62">A3</font></i></a>, <a class="txt" href="gcd_1.html#E8:82_1_1_4"><i><font color="Green" title="E69">A22</font></i></a>, <a class="txt" href="gcd_1.html#E9:82_1_1_4"><i><font color="Green" title="E70">A23</font></i></a>, <a class="ref" href="gcd_1.html#T11" target="_self" title="GCD_1:th.11">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">r2</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
;<br/><b>hence </b><a NAME="E11:82_1_1_4"/>
<span class="p1">(<span class="default"><a href="gcd_1.html#K8" title="GCD_1:func.8">mult1</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K9" title="GCD_1:func.9">mult2</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span>
 <b>by </b><i><a class="txt" href="gcd_1.html#E1:82_1_1_4"><i><font color="Green" title="E63">A16</font></i></a>, <a class="txt" href="gcd_1.html#E2:82_1_1_4"><i><font color="Green" title="E64">A17</font></i></a>, <a class="txt" href="gcd_1.html#E6:82_1_1_4"><i><font color="Green" title="E67">A20</font></i></a>, <a class="ref" href="gcd_1.html#D18" target="_self" title="GCD_1:def.18">Def18</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_1_1_5"><b>case </b></a><a NAME="E1:82_1_1_5"/><i><font color="Green" title="E63">A24</font></i>: 
( not <font color="Maroon" title="c3">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> &amp; not <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> &amp; (  not <font color="Maroon" title="c4">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> or  not <font color="Maroon" title="c6">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> ) &amp; (  not <font color="Maroon" title="c6">s2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> or  not <font color="Maroon" title="c4">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> ) &amp; (  not <font color="Maroon" title="c4">r2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font> or  not <font color="Maroon" title="c6">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> ) )
 ;<br/><div class="add"><a NAME="E2:82_1_1_5"/><b>then </b><i><font color="Green" title="E64">A25</font></i>: 
 <a href="gcd_1.html#K9" title="GCD_1:func.9">mult2</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="gcd_1.html#E3:82"><i><font color="Green" title="E61">A2</font></i></a>, <a class="ref" href="gcd_1.html#D19" target="_self" title="GCD_1:def.19">Def19</a></i>;<br/><a NAME="E3:82_1_1_5"/><i><font color="Green" title="E65">A26</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c3">r1</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/><a NAME="E4:82_1_1_5"/><i><font color="Green" title="E66">A27</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c5">s1</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/><a NAME="E5:82_1_1_5"/><b>then </b><i><font color="Green" title="E67">A28</font></i>: 
<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font>
 <b>by </b><i><a class="txt" href="gcd_1.html#E3:82_1_1_5"><i><font color="Green" title="E65">A26</font></i></a>, <a class="ref" href="gcd_1.html#T3" target="_self" title="GCD_1:th.3">Th3</a></i>;<br/><a NAME="E6:82_1_1_5"/><b>then </b><i><font color="Green" title="E68">A29</font></i>: 
<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">r2</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#T7" target="_self" title="GCD_1:th.7">Th7</a></i>;<br/><a NAME="E7:82_1_1_5"/><b>then </b><i><font color="Green" title="E69">A30</font></i>: 
<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">r2</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#T7" target="_self" title="GCD_1:th.7">Th7</a></i>;<br/><a NAME="E8:82_1_1_5"/><i><font color="Green" title="E70">A31</font></i>: 
<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="txt" href="gcd_1.html#E4:82"><i><font color="Green" title="E62">A3</font></i></a>, <a class="ref" href="vectsp_2.html#D5" title="VECTSP_2:def.5">VECTSP_2:def 5</a></i>;<br/><i><font color="Green" title="E71">A32</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="gcd_1.html#E4:82"><i><font color="Green" title="E62">A3</font></i></a>, <a class="txt" href="gcd_1.html#E3:82_1_1_5"><i><font color="Green" title="E65">A26</font></i></a>, <a class="txt" href="gcd_1.html#E4:82_1_1_5"><i><font color="Green" title="E66">A27</font></i></a>, <a class="ref" href="gcd_1.html#T14" target="_self" title="GCD_1:th.14">Th14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">r2</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">r2</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font>
<b>by </b><i><a class="txt" href="gcd_1.html#E5:82_1_1_5"><i><font color="Green" title="E67">A28</font></i></a>, <a class="txt" href="gcd_1.html#E6:82_1_1_5"><i><font color="Green" title="E68">A29</font></i></a>, <a class="txt" href="gcd_1.html#E8:82_1_1_5"><i><font color="Green" title="E70">A31</font></i></a>, <a class="ref" href="gcd_1.html#T11" target="_self" title="GCD_1:th.11">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">r2</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="gcd_1.html#E6:82_1_1_5"><i><font color="Green" title="E68">A29</font></i></a>, <a class="txt" href="gcd_1.html#E7:82_1_1_5"><i><font color="Green" title="E69">A30</font></i></a>, <a class="txt" href="gcd_1.html#E8:82_1_1_5"><i><font color="Green" title="E70">A31</font></i></a>, <a class="ref" href="gcd_1.html#T11" target="_self" title="GCD_1:th.11">Th11</a></i>
;<br/><a NAME="E10:82_1_1_5"/><i><font color="Green" title="E72">A33</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c4">r2</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/><a NAME="E11:82_1_1_5"/><i><font color="Green" title="E73">A34</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c6">s2</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/><a NAME="E12:82_1_1_5"/><b>then </b><i><font color="Green" title="E74">A35</font></i>: 
<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font>
 <b>by </b><i><a class="txt" href="gcd_1.html#E10:82_1_1_5"><i><font color="Green" title="E72">A33</font></i></a>, <a class="ref" href="gcd_1.html#T3" target="_self" title="GCD_1:th.3">Th3</a></i>;<br/><a NAME="E13:82_1_1_5"/><b>then </b><i><font color="Green" title="E75">A36</font></i>: 
<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">r1</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#T7" target="_self" title="GCD_1:th.7">Th7</a></i>;<br/><a NAME="E14:82_1_1_5"/><b>then </b><i><font color="Green" title="E76">A37</font></i>: 
<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">r1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#T7" target="_self" title="GCD_1:th.7">Th7</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span>
<b>by </b><i><a class="txt" href="gcd_1.html#E4:82"><i><font color="Green" title="E62">A3</font></i></a>, <a class="txt" href="gcd_1.html#E10:82_1_1_5"><i><font color="Green" title="E72">A33</font></i></a>, <a class="txt" href="gcd_1.html#E11:82_1_1_5"><i><font color="Green" title="E73">A34</font></i></a>, <a class="ref" href="gcd_1.html#T14" target="_self" title="GCD_1:th.14">Th14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">r1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">r1</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font>
<b>by </b><i><a class="txt" href="gcd_1.html#E8:82_1_1_5"><i><font color="Green" title="E70">A31</font></i></a>, <a class="txt" href="gcd_1.html#E12:82_1_1_5"><i><font color="Green" title="E74">A35</font></i></a>, <a class="txt" href="gcd_1.html#E13:82_1_1_5"><i><font color="Green" title="E75">A36</font></i></a>, <a class="ref" href="gcd_1.html#T11" target="_self" title="GCD_1:th.11">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">r1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="gcd_1.html#E8:82_1_1_5"><i><font color="Green" title="E70">A31</font></i></a>, <a class="txt" href="gcd_1.html#E13:82_1_1_5"><i><font color="Green" title="E75">A36</font></i></a>, <a class="txt" href="gcd_1.html#E14:82_1_1_5"><i><font color="Green" title="E76">A37</font></i></a>, <a class="ref" href="gcd_1.html#T11" target="_self" title="GCD_1:th.11">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">r2</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">r2</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">r2</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
;<br/><b>hence </b><a NAME="E16:82_1_1_5"/>
<span class="p1">(<span class="default"><a href="gcd_1.html#K8" title="GCD_1:func.8">mult1</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K9" title="GCD_1:func.9">mult2</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span>
 <b>by </b><i><a class="txt" href="gcd_1.html#E1:82_1_1_5"><i><font color="Green" title="E63">A24</font></i></a>, <a class="txt" href="gcd_1.html#E2:82_1_1_5"><i><font color="Green" title="E64">A25</font></i></a>, <a class="txt" href="gcd_1.html#E9:82_1_1_5"><i><font color="Green" title="E71">A32</font></i></a>, <a class="ref" href="gcd_1.html#D18" target="_self" title="GCD_1:def.18">Def18</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E6:82"/>
<span class="p1">(<span class="default"><a href="gcd_1.html#K8" title="GCD_1:func.8">mult1</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">s2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K9" title="GCD_1:func.9">mult2</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">s1</font></span>)</span>
 ;<br/>


</div>
