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<b>let </b><font color="Maroon">c<sub>11</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>14</sub></font> be    <a href="trees_4.html#M1">FinSequence</a> of  <a href="wsierp_1.html#K6">INT</a> ;<br/>





<b>assume </b><a NAME="E1:10"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3 &amp; <font color="Maroon">c<sub>14</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>15</sub></font> =  <a href="scmp_gcd.html#K2">GBP</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>16</sub></font> = <a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0;<br/>
<b>set </b><font color="Maroon">c<sub>17</sub></font> = <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0;<br/>
<b>set </b><font color="Maroon">c<sub>18</sub></font> = <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>19</sub></font> = <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>20</sub></font> =  <a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>11</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>21</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>22</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>23</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>24</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>25</sub></font> =  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>;<br/>
<a NAME="E2:10"/><i><font color="Green">E11</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>;<br/>
<a NAME="E3:10"/><i><font color="Green">E12</font></i>: 
 <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> 1
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<i><font color="Green">E13</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="scpinvar.html#E2:10"><i><font color="Green">E11</font></i></a>, <a class="txt" href="scpinvar.html#E3:10"><i><font color="Green">E12</font></i></a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<i><font color="Green">E14</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
0
<b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<a NAME="E6:10"/><i><font color="Green">E15</font></i>: 
 <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> 2
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<i><font color="Green">E16</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="scpinvar.html#E4:10"><i><font color="Green">E13</font></i></a>, <a class="txt" href="scpinvar.html#E6:10"><i><font color="Green">E15</font></i></a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<a NAME="E8:10"/><i><font color="Green">E17</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> 2
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<i><font color="Green">E18</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="scpinvar.html#E5:10"><i><font color="Green">E14</font></i></a>, <a class="txt" href="scpinvar.html#E8:10"><i><font color="Green">E17</font></i></a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<i><font color="Green">E19</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<a NAME="E11:10"/><i><font color="Green">E20</font></i>: 
 <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> 3
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<i><font color="Green">E21</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="scpinvar.html#E7:10"><i><font color="Green">E16</font></i></a>, <a class="txt" href="scpinvar.html#E11:10"><i><font color="Green">E20</font></i></a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<a NAME="E13:10"/><i><font color="Green">E22</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> 3
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<i><font color="Green">E23</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="scpinvar.html#E9:10"><i><font color="Green">E18</font></i></a>, <a class="txt" href="scpinvar.html#E13:10"><i><font color="Green">E22</font></i></a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<a NAME="E15:10"/><i><font color="Green">E24</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> 2 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> 3
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<i><font color="Green">E25</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="scpinvar.html#E10:10"><i><font color="Green">E19</font></i></a>, <a class="txt" href="scpinvar.html#E15:10"><i><font color="Green">E24</font></i></a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<i><font color="Green">E26</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_10"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>26</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:10_10"/><i><font color="Green">E27</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>26</sub></font> &amp; <font color="Maroon">c<sub>26</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>14</sub></font> )
 ;<br/><a NAME="E2:10_10"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:10"><i><font color="Green">E10</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:10_10"/>
<font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:10_10"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E4:10_10"/><b>then </b><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 4
 <b>by </b><i><a class="txt" href="scpinvar.html#E2:10_10"><i><font color="Green">E28</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E5:10_10"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 3
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E6:10_10"/><b>then </b><i><font color="Green">E30</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> 3
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><a NAME="E7:10_10"/>
<font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 <b>by </b><i><a class="txt" href="scpinvar.html#E4:10_10"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E8:10_10"/><b>then </b><i><font color="Green">E31</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> 2
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><a NAME="E9:10_10"/>
<font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i><a class="txt" href="scpinvar.html#E4:10_10"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E10:10_10"/><b>then </b><i><font color="Green">E32</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> 1
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><a NAME="E11:10_10"/>
<font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="scpinvar.html#E4:10_10"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E12:10_10"/><b>then </b><i><font color="Green">E33</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K2">GBP</a> 
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E6:10_10"><i><font color="Green">E30</font></i></a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E8:10_10"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E10:10_10"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E12:10_10"><i><font color="Green">E33</font></i></a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
<font color="Maroon">c<sub>11</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
<br/>.= 
<font color="Maroon">c<sub>14</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scpinvar.html#E1:10"><i><font color="Green">E10</font></i></a>, <a class="txt" href="scpinvar.html#E1:10_10"><i><font color="Green">E27</font></i></a>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E19:10"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/>
<a NAME="E20:10"/><b>then </b><i><font color="Green">E27</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2">while&lt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="wsierp_1.html#K7">Sum</a> <font color="Maroon">c<sub>14</sub></font> &amp;  <a href="scmpds_8.html#K2">while&lt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font> &amp;  <a href="scmpds_8.html#K2">while&lt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font> )
 
<b>by </b><i><a class="txt" href="scpinvar.html#E1:10"><i><font color="Green">E10</font></i></a>, <a class="txt" href="scpinvar.html#E12:10"><i><font color="Green">E21</font></i></a>, <a class="txt" href="scpinvar.html#E14:10"><i><font color="Green">E23</font></i></a>, <a class="txt" href="scpinvar.html#E16:10"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scpinvar.html#E17:10"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scpinvar.html#E12"><i><font color="Green">Lemma8</font></i></a></i>;<br/>
<b>thus </b><a NAME="E21:10"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K1" target="_self">sum</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="wsierp_1.html#K7">Sum</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="scpinvar.html#E20:10"><i><font color="Green">E27</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>;<br/>

<b>thus </b><a NAME="E22:10"/>
 <a href="scpinvar.html#K1" target="_self">sum</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="scpinvar.html#E20:10"><i><font color="Green">E27</font></i></a>, <a class="ref" href="scpisort.html#T10">SCPISORT:10</a></i>;<br/>


</div>
