let P be Instruction-Sequence of SCMPDS; for s being 0 -started State of SCMPDS st s . (intpos 1) > 0 & s . (intpos 2) > 0 holds
( (IExec (((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2)))))),P,s)) . (intpos 1) = (s . (intpos 1)) gcd (s . (intpos 2)) & (IExec (((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2)))))),P,s)) . (intpos 2) = (s . (intpos 1)) gcd (s . (intpos 2)) & (((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))) is_closed_on s,P & (((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))) is_halting_on s,P )
let s be 0 -started State of SCMPDS; ( s . (intpos 1) > 0 & s . (intpos 2) > 0 implies ( (IExec (((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2)))))),P,s)) . (intpos 1) = (s . (intpos 1)) gcd (s . (intpos 2)) & (IExec (((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2)))))),P,s)) . (intpos 2) = (s . (intpos 1)) gcd (s . (intpos 2)) & (((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))) is_closed_on s,P & (((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))) is_halting_on s,P ) )
A1:
Initialize s = s
by MEMSTR_0:44;
assume A2:
( s . (intpos 1) > 0 & s . (intpos 2) > 0 )
; ( (IExec (((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2)))))),P,s)) . (intpos 1) = (s . (intpos 1)) gcd (s . (intpos 2)) & (IExec (((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2)))))),P,s)) . (intpos 2) = (s . (intpos 1)) gcd (s . (intpos 2)) & (((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))) is_closed_on s,P & (((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))) is_halting_on s,P )
set t0 = s;
set Q0 = P;
set t1 = IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s);
set t2 = IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s);
set Q1 = P;
set t3 = Exec ((GBP := 0),s);
set a = GBP ;
A3: (Exec ((GBP := 0),s)) . (intpos 1) =
s . (intpos 1)
by AMI_3:10, SCMPDS_2:45
.=
s . (intpos 1)
;
A4:
(Exec ((GBP := 0),s)) . GBP = 0
by SCMPDS_2:45;
then A5:
DataLoc (((Exec ((GBP := 0),s)) . GBP),3) = intpos (0 + 3)
by SCMP_GCD:1;
1 <> |.(((Exec ((GBP := 0),s)) . GBP) + 3).|
by A4, ABSVALUE:def 1;
then A6:
intpos 1 <> DataLoc (((Exec ((GBP := 0),s)) . GBP),3)
by XTUPLE_0:1;
A7: (IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)) . (intpos 1) =
(Exec (((GBP,3) := (GBP,1)),(Exec ((GBP := 0),s)))) . (intpos 1)
by SCMPDS_5:42
.=
s . (intpos 1)
by A3, A6, SCMPDS_2:47
;
A8: (Exec ((GBP := 0),s)) . (intpos 2) =
s . (intpos 2)
by AMI_3:10, SCMPDS_2:45
.=
s . (intpos 2)
;
A9: (IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)) . (intpos 3) =
(Exec (((GBP,3) := (GBP,1)),(Exec ((GBP := 0),s)))) . (intpos 3)
by SCMPDS_5:42
.=
(Exec ((GBP := 0),s)) . (DataLoc (((Exec ((GBP := 0),s)) . GBP),1))
by A5, SCMPDS_2:47
.=
s . (intpos 1)
by A4, A3, SCMP_GCD:1
;
2 <> |.(((Exec ((GBP := 0),s)) . GBP) + 3).|
by A4, ABSVALUE:def 1;
then A10:
intpos 2 <> DataLoc (((Exec ((GBP := 0),s)) . GBP),3)
by XTUPLE_0:1;
A11: (IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)) . (intpos 2) =
(Exec (((GBP,3) := (GBP,1)),(Exec ((GBP := 0),s)))) . (intpos 2)
by SCMPDS_5:42
.=
s . (intpos 2)
by A8, A10, SCMPDS_2:47
;
0 <> |.(((Exec ((GBP := 0),s)) . GBP) + 3).|
by A4, ABSVALUE:def 1;
then A12:
GBP <> DataLoc (((Exec ((GBP := 0),s)) . GBP),3)
by XTUPLE_0:1;
A13: (IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)) . GBP =
(Exec (((GBP,3) := (GBP,1)),(Exec ((GBP := 0),s)))) . GBP
by SCMPDS_5:42
.=
0
by A4, A12, SCMPDS_2:47
;
then A14:
DataLoc (((IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)) . GBP),3) = intpos (0 + 3)
by SCMP_GCD:1;
0 <> |.(((IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)) . GBP) + 3).|
by A13, ABSVALUE:def 1;
then A15:
GBP <> DataLoc (((IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)) . GBP),3)
by XTUPLE_0:1;
A16: (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)) . GBP =
(Exec ((SubFrom (GBP,3,GBP,2)),(IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)))) . GBP
by SCMPDS_5:41
.=
0
by A13, A15, SCMPDS_2:50
;
1 <> |.(((IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)) . GBP) + 3).|
by A13, ABSVALUE:def 1;
then A17:
intpos 1 <> DataLoc (((IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)) . GBP),3)
by XTUPLE_0:1;
A18: (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)) . (intpos 1) =
(Exec ((SubFrom (GBP,3,GBP,2)),(IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)))) . (intpos 1)
by SCMPDS_5:41
.=
s . (intpos 1)
by A7, A17, SCMPDS_2:50
;
2 <> |.(((IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)) . GBP) + 3).|
by A13, ABSVALUE:def 1;
then A19:
intpos 2 <> DataLoc (((IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)) . GBP),3)
by XTUPLE_0:1;
A20: (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)) . (intpos 2) =
(Exec ((SubFrom (GBP,3,GBP,2)),(IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)))) . (intpos 2)
by SCMPDS_5:41
.=
s . (intpos 2)
by A11, A19, SCMPDS_2:50
;
A21:
(Initialize (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s))) . (intpos 1) = (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)) . (intpos 1)
by SCMPDS_5:15;
A22:
(Initialize (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s))) . (intpos 2) = (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)) . (intpos 2)
by SCMPDS_5:15;
A23: (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)) . (intpos 3) =
(Exec ((SubFrom (GBP,3,GBP,2)),(IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)))) . (intpos 3)
by SCMPDS_5:41
.=
((IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)) . (intpos 3)) - ((IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)) . (DataLoc (((IExec (((GBP := 0) ';' ((GBP,3) := (GBP,1))),P,s)) . GBP),2)))
by A14, SCMPDS_2:50
.=
((IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)) . (intpos 1)) - ((IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)) . (intpos 2))
by A13, A11, A9, A18, A20, SCMP_GCD:1
;
A24:
(Initialize (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s))) . GBP = (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)) . GBP
by SCMPDS_5:15;
A25:
(Initialize (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s))) . (intpos 3) = (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)) . (intpos 3)
by SCMPDS_5:15;
A26:
( while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2)))) is_closed_on Initialize (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)),P & while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2)))) is_halting_on Initialize (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)),P )
by A2, A16, A18, A20, Lm13, A21, A22, A23, A24, A25;
A27:
while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2)))) is_closed_on IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s),P
proof
for
k being
Nat holds
IC (Comput ((P +* (stop (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))))),(Initialize (Initialize (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)))),k)) in dom (stop (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))))
by A26, SCMPDS_6:def 2;
hence
while<>0 (
GBP,3,
(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))
is_closed_on IExec (
(((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),
P,
s),
P
by SCMPDS_6:def 2;
verum
end;
A28:
while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2)))) is_halting_on IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s),P
proof
P +* (stop (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2)))))) halts_on Initialize (Initialize (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)))
by A26, SCMPDS_6:def 3;
hence
while<>0 (
GBP,3,
(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))
is_halting_on IExec (
(((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),
P,
s),
P
by SCMPDS_6:def 3;
verum
end;
(IExec ((while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))),P,(Initialize (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s))))) . (intpos 1) = ((IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)) . (intpos 1)) gcd ((IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)) . (intpos 2))
by A2, A16, A18, A20, A23, Lm13, A21, A22, A25, A24;
hence
(IExec (((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2)))))),P,s)) . (intpos 1) = (s . (intpos 1)) gcd (s . (intpos 2))
by A18, A20, A27, A28, SCPISORT:7; ( (IExec (((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2)))))),P,s)) . (intpos 2) = (s . (intpos 1)) gcd (s . (intpos 2)) & (((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))) is_closed_on s,P & (((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))) is_halting_on s,P )
(IExec ((while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))),P,(Initialize (IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s))))) . (intpos 2) = ((IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)) . (intpos 1)) gcd ((IExec ((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))),P,s)) . (intpos 2))
by A2, A16, A18, A20, A23, Lm13, A21, A22, A25, A24;
hence
(IExec (((((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2)))))),P,s)) . (intpos 2) = (s . (intpos 1)) gcd (s . (intpos 2))
by A18, A20, A27, A28, SCPISORT:7; ( (((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))) is_closed_on s,P & (((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))) is_halting_on s,P )
thus
( (((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))) is_closed_on s,P & (((GBP := 0) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))) ';' (while<>0 (GBP,3,(((if>0 (GBP,3,(Load (SubFrom (GBP,1,GBP,2))),(Load (SubFrom (GBP,2,GBP,1))))) ';' ((GBP,3) := (GBP,1))) ';' (SubFrom (GBP,3,GBP,2))))) is_halting_on s,P )
by A27, A1, A28, SCPISORT:9; verum