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<b>let </b><font color="Maroon">c<sub>13</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:15"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="ami_3.html#R1">starts_at</a>  <a href="ami_3.html#K16">il.</a> 0
 <b>and </b><br/><a NAME="E2:15"/><i><font color="Green">E15</font></i>: 
 <a href="ami_4.html#K1" target="_self">Euclide-Algorithm</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E3:15"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>and </b><br/><a NAME="E4:15"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font>
 <b>and </b><br/><a NAME="E5:15"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>and </b><br/><a NAME="E6:15"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:15_1_1"/>
( <font color="Maroon">c<sub>14</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>15</sub></font> or <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> or <font color="Maroon">c<sub>15</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>14</sub></font> )
 </span><b>by </b><i><a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1_1"><b>case </b></a><a NAME="E1:15_1_1_1"/>
<font color="Maroon">c<sub>14</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_1_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="int_2.html#K3">gcd</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="ami_4.html#E1:15"><i><font color="Green">E14</font></i></a>, <a class="txt" href="ami_4.html#E2:15"><i><font color="Green">E15</font></i></a>, <a class="txt" href="ami_4.html#E3:15"><i><font color="Green">E16</font></i></a>, <a class="txt" href="ami_4.html#E4:15"><i><font color="Green">E17</font></i></a>, <a class="txt" href="ami_4.html#E6:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="ami_4.html#E14"><i><font color="Green">Lemma12</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1_2"><b>case </b></a><a NAME="E1:15_1_1_2"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/><div class="add"><b>take </b><font color="Maroon">c<sub>16</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4;<br/><b>reconsider </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>15</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="ami_4.html#E5:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="ami_4.html#E6:15"><i><font color="Green">E19</font></i></a>, <a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><a NAME="E3:15_1_1_2"/>
(  <a href="int_2.html#K1">abs</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> &amp;  <a href="int_2.html#K1">abs</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> )
 <b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/><b>then </b><i><font color="Green">E21</font></i>: <font color="Maroon">c<sub>14</sub></font> <a href="int_1.html#K6">mod</a> <font color="Maroon">c<sub>15</sub></font> = 
<font color="Maroon">c<sub>17</sub></font> <a href="nat_1.html#K4">mod</a> <font color="Maroon">c<sub>18</sub></font>
<b>by </b><i><a class="ref" href="ami_4.html#T2" target="_self">Th2</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="ami_4.html#E1:15_1_1_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="nat_1.html#T77">NAT_1:77</a></i>
;<br/><a NAME="E5:15_1_1_2"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K2">*</a> 0</span>)</span> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>;<br/><a NAME="E6:15_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="ami_4.html#E1:15"><i><font color="Green">E14</font></i></a>, <a class="txt" href="ami_4.html#E2:15"><i><font color="Green">E15</font></i></a>, <a class="txt" href="ami_4.html#E3:15"><i><font color="Green">E16</font></i></a>, <a class="txt" href="ami_4.html#E4:15"><i><font color="Green">E17</font></i></a>, <a class="txt" href="ami_4.html#E5:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="ami_4.html#E6:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="ami_4.html#E4:15_1_1_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="ami_4.html#E13"><i><font color="Green">Lemma11</font></i></a></i>;<br/><a NAME="E7:15_1_1_2"/><b>then </b>
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 4
 <b>by </b><i><a class="txt" href="ami_4.html#E1:15"><i><font color="Green">E14</font></i></a>, <a class="txt" href="ami_4.html#E2:15"><i><font color="Green">E15</font></i></a>, <a class="txt" href="ami_4.html#E3:15"><i><font color="Green">E16</font></i></a>, <a class="txt" href="ami_4.html#E4:15"><i><font color="Green">E17</font></i></a>, <a class="txt" href="ami_4.html#E5:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="ami_4.html#E6:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="ami_4.html#E5:15_1_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="ami_4.html#E12"><i><font color="Green">Lemma10</font></i></a></i>;<br/><a NAME="E8:15_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> <a href="ami_3.html#R2">halts_at</a>  <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="ami_4.html#E2:15"><i><font color="Green">E15</font></i></a>, <a class="txt" href="ami_4.html#E6"><i><font color="Green">Lemma4</font></i></a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> = 
<font color="Maroon">c<sub>16</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#T44">AMI_3:44</a></i>
<br/>.= 
<font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="ami_4.html#E1:15"><i><font color="Green">E14</font></i></a>, <a class="txt" href="ami_4.html#E2:15"><i><font color="Green">E15</font></i></a>, <a class="txt" href="ami_4.html#E3:15"><i><font color="Green">E16</font></i></a>, <a class="txt" href="ami_4.html#E4:15"><i><font color="Green">E17</font></i></a>, <a class="txt" href="ami_4.html#E5:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="ami_4.html#E6:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="ami_4.html#E5:15_1_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="ami_4.html#E13"><i><font color="Green">Lemma11</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="int_2.html#K1">abs</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="nat_1.html#K8">hcf</a> <span class="p1">(<span class="default"><a href="int_2.html#K1">abs</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E6:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="ami_4.html#E1:15_1_1_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
<br/>.= 
<font color="Maroon">c<sub>14</sub></font> <a href="int_2.html#K3">gcd</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="ref" href="int_2.html#D3">INT_2:def 3</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1_3"><b>case </b></a><a NAME="E1:15_1_1_3"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>14</sub></font>
 ;<br/><div class="add"><b>take </b><font color="Maroon">c<sub>16</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4;<br/><b>reconsider </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>15</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="ami_4.html#E5:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="ami_4.html#E6:15"><i><font color="Green">E19</font></i></a>, <a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><a NAME="E3:15_1_1_3"/>
(  <a href="int_2.html#K1">abs</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> &amp;  <a href="int_2.html#K1">abs</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> )
 <b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/><b>then </b><i><font color="Green">E21</font></i>: <font color="Maroon">c<sub>14</sub></font> <a href="int_1.html#K6">mod</a> <font color="Maroon">c<sub>15</sub></font> = 
<font color="Maroon">c<sub>17</sub></font> <a href="nat_1.html#K4">mod</a> <font color="Maroon">c<sub>18</sub></font>
<b>by </b><i><a class="ref" href="ami_4.html#T2" target="_self">Th2</a></i>
<br/>.= 
<font color="Maroon">c<sub>17</sub></font>
<b>by </b><i><a class="txt" href="ami_4.html#E1:15_1_1_3"><i><font color="Green">E20</font></i></a>, <a class="ref" href="nat_1.html#T76">NAT_1:76</a></i>
;<br/><a NAME="E5:15_1_1_3"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K2">*</a> 0</span>)</span> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>;<br/><a NAME="E6:15_1_1_3"/><b>then </b><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>16</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> )
 <b>by </b><i><a class="txt" href="ami_4.html#E1:15"><i><font color="Green">E14</font></i></a>, <a class="txt" href="ami_4.html#E2:15"><i><font color="Green">E15</font></i></a>, <a class="txt" href="ami_4.html#E3:15"><i><font color="Green">E16</font></i></a>, <a class="txt" href="ami_4.html#E4:15"><i><font color="Green">E17</font></i></a>, <a class="txt" href="ami_4.html#E5:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="ami_4.html#E6:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="ami_4.html#E4:15_1_1_3"><i><font color="Green">E21</font></i></a>, <a class="txt" href="ami_4.html#E13"><i><font color="Green">Lemma11</font></i></a></i>;<br/><a NAME="E7:15_1_1_3"/><b>then </b>
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 0
 <b>by </b><i><a class="txt" href="ami_4.html#E1:15"><i><font color="Green">E14</font></i></a>, <a class="txt" href="ami_4.html#E2:15"><i><font color="Green">E15</font></i></a>, <a class="txt" href="ami_4.html#E3:15"><i><font color="Green">E16</font></i></a>, <a class="txt" href="ami_4.html#E4:15"><i><font color="Green">E17</font></i></a>, <a class="txt" href="ami_4.html#E5:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="ami_4.html#E6:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="ami_4.html#E5:15_1_1_3"><i><font color="Green">E22</font></i></a>, <a class="txt" href="ami_4.html#E12"><i><font color="Green">Lemma10</font></i></a></i>;<br/><a NAME="E8:15_1_1_3"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="ami_3.html#R1">starts_at</a>  <a href="ami_3.html#K16">il.</a> 0
 <b>by </b><i><a class="ref" href="ami_3.html#D14">AMI_3:def 14</a></i>;<br/><a NAME="E9:15_1_1_3"/><i><font color="Green">E25</font></i>: 
 <a href="ami_4.html#K1" target="_self">Euclide-Algorithm</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="ami_4.html#E2:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="ami_3.html#T43">AMI_3:43</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>19</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E11:15_1_1_3"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="ami_3.html#R2">halts_at</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_4.html#E5:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="ami_4.html#E1:15_1_1_3"><i><font color="Green">E20</font></i></a>, <a class="txt" href="ami_4.html#E6:15_1_1_3"><i><font color="Green">E23</font></i></a>, <a class="txt" href="ami_4.html#E8:15_1_1_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="ami_4.html#E14"><i><font color="Green">Lemma12</font></i></a></i>;<br/><a NAME="E12:15_1_1_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>;<br/><a NAME="E13:15_1_1_3"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="ami_3.html#R2">halts_at</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_4.html#E11:15_1_1_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="ami_3.html#T48">AMI_3:48</a></i>;<br/><a NAME="E14:15_1_1_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="int_2.html#K3">gcd</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="ami_4.html#E5:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="ami_4.html#E1:15_1_1_3"><i><font color="Green">E20</font></i></a>, <a class="txt" href="ami_4.html#E6:15_1_1_3"><i><font color="Green">E23</font></i></a>, <a class="txt" href="ami_4.html#E8:15_1_1_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="ami_4.html#E9:15_1_1_3"><i><font color="Green">E25</font></i></a>, <a class="txt" href="ami_4.html#E14"><i><font color="Green">Lemma12</font></i></a></i>;<br/><b>hence </b><a NAME="E15:15_1_1_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="int_2.html#K3">gcd</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="ami_4.html#E13:15_1_1_3"><i><font color="Green">E27</font></i></a>, <a class="ref" href="ami_3.html#T47">AMI_3:47</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E8:15"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="int_2.html#K3">gcd</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/>


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