let P be Instruction-Sequence of SCMPDS; :: thesis:
set a = GBP ;
let s be 0 -started State of SCMPDS; :: thesis:
let md, me be Nat; :: thesis:
assume that
A1: s . (intpos 2) = md and
A2: s . (intpos 3) = me and
A3: md >= 8 and
A4: me >= 8 and
A5: s . GBP = 0 ; :: thesis:
set t0 = s;
set t1 = IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s);
set Q1 = P;
set t2 = IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s);
set t3 = IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s);
set t4 = Exec (((GBP,5) := (GBP,7)),s);
A6: s . GBP = 0 by A5;
A7: DataLoc ((s . GBP),5) = intpos (0 + 5) by A5, SCMP_GCD:1;
then A8: (Exec (((GBP,5) := (GBP,7)),s)) . GBP = 0 by A5, AMI_3:10, SCMPDS_2:47;
then A9: DataLoc (((Exec (((GBP,5) := (GBP,7)),s)) . GBP),7) = intpos (0 + 7) by SCMP_GCD:1;
A10: (Exec (((GBP,5) := (GBP,7)),s)) . (intpos 2) = md by A7, A1, AMI_3:10, SCMPDS_2:47;
A11: (IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)) . (intpos 2) = (Exec ((AddTo (GBP,7,(- 1))),(Exec (((GBP,5) := (GBP,7)),s)))) . (intpos 2) by SCMPDS_5:42
.= md by A10, A9, AMI_3:10, SCMPDS_2:48 ;
then A12: DataLoc (((IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)) . (intpos 2)),0) = intpos (md + 0) by SCMP_GCD:1;
A13: (IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)) . GBP = (Exec ((AddTo (GBP,7,(- 1))),(Exec (((GBP,5) := (GBP,7)),s)))) . GBP by SCMPDS_5:42
.= 0 by A8, A9, AMI_3:10, SCMPDS_2:48 ;
then A14: DataLoc (((IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)) . GBP),6) = intpos (0 + 6) by SCMP_GCD:1;
A15: (Exec (((GBP,5) := (GBP,7)),s)) . (intpos 3) = me by A7, A2, AMI_3:10, SCMPDS_2:47;
A16: (IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)) . (intpos 3) = (Exec ((AddTo (GBP,7,(- 1))),(Exec (((GBP,5) := (GBP,7)),s)))) . (intpos 3) by SCMPDS_5:42
.= me by A15, A9, AMI_3:10, SCMPDS_2:48 ;
A17: (Exec (((GBP,5) := (GBP,7)),s)) . (intpos 7) = s . (intpos 7) by A7, AMI_3:10, SCMPDS_2:47;
set t01 = Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s));
set jj7 = (GBP,7) := 0;
set t5 = Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))));
A18: (IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)) . (intpos 3) = (Exec (((GBP,6) := ((intpos 2),0)),(IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)))) . (intpos 3) by SCMPDS_5:41
.= me by A16, A14, AMI_3:10, SCMPDS_2:47 ;
A19: (IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)) . GBP = (Exec (((GBP,6) := ((intpos 2),0)),(IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)))) . GBP by SCMPDS_5:41
.= 0 by A13, A14, AMI_3:10, SCMPDS_2:47 ;
then A20: DataLoc (((IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)) . GBP),6) = intpos (0 + 6) by SCMP_GCD:1;
A21: (Exec (((GBP,5) := (GBP,7)),s)) . (intpos 4) = s . (intpos 4) by A7, AMI_3:10, SCMPDS_2:47;
A22: (IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)) . (intpos 4) = (Exec ((AddTo (GBP,7,(- 1))),(Exec (((GBP,5) := (GBP,7)),s)))) . (intpos 4) by SCMPDS_5:42
.= s . (intpos 4) by A21, A9, AMI_3:10, SCMPDS_2:48 ;
A23: (Exec (((GBP,5) := (GBP,7)),s)) . (intpos 1) = s . (intpos 1) by A7, AMI_3:10, SCMPDS_2:47;
A24: (IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)) . (intpos 1) = (Exec ((AddTo (GBP,7,(- 1))),(Exec (((GBP,5) := (GBP,7)),s)))) . (intpos 1) by SCMPDS_5:42
.= s . (intpos 1) by A23, A9, AMI_3:10, SCMPDS_2:48 ;
A25: (IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)) . (intpos 1) = (Exec (((GBP,6) := ((intpos 2),0)),(IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)))) . (intpos 1) by SCMPDS_5:41
.= s . (intpos 1) by A24, A14, AMI_3:10, SCMPDS_2:47 ;
(IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s)) . (intpos 1) = (Exec ((SubFrom (GBP,6,(intpos 3),0)),(IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)))) . (intpos 1) by SCMPDS_5:41
.= s . (intpos 1) by A25, A20, AMI_3:10, SCMPDS_2:50 ;
then A26: (Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . (intpos 1) = s . (intpos 1) by SCMPDS_5:15;
A27: (IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)) . (intpos 4) = (Exec (((GBP,6) := ((intpos 2),0)),(IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)))) . (intpos 4) by SCMPDS_5:41
.= s . (intpos 4) by A22, A14, AMI_3:10, SCMPDS_2:47 ;
(IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s)) . (intpos 4) = (Exec ((SubFrom (GBP,6,(intpos 3),0)),(IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)))) . (intpos 4) by SCMPDS_5:41
.= s . (intpos 4) by A27, A20, AMI_3:10, SCMPDS_2:50 ;
then A28: (Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . (intpos 4) = s . (intpos 4) by SCMPDS_5:15;
A29: (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s)) . GBP = (Exec ((SubFrom (GBP,6,(intpos 3),0)),(IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)))) . GBP by SCMPDS_5:41
.= 0 by A19, A20, AMI_3:10, SCMPDS_2:50 ;
then A30: (Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . GBP = 0 by SCMPDS_5:15;
then A31: DataLoc (((Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . GBP),7) = intpos (0 + 7) by SCMP_GCD:1;
DataLoc ((s . GBP),7) = intpos (0 + 7) by A6, SCMP_GCD:1;
then A32: (Exec (((GBP,5) := (GBP,7)),s)) . (intpos 5) = s . (intpos 7) by A7, SCMPDS_2:47;
A33: (IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)) . (intpos 5) = (Exec ((AddTo (GBP,7,(- 1))),(Exec (((GBP,5) := (GBP,7)),s)))) . (intpos 5) by SCMPDS_5:42
.= s . (intpos 7) by A32, A9, AMI_3:10, SCMPDS_2:48 ;
A34: (IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)) . (intpos 5) = (Exec (((GBP,6) := ((intpos 2),0)),(IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)))) . (intpos 5) by SCMPDS_5:41
.= s . (intpos 7) by A33, A14, AMI_3:10, SCMPDS_2:47 ;
(IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s)) . (intpos 5) = (Exec ((SubFrom (GBP,6,(intpos 3),0)),(IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)))) . (intpos 5) by SCMPDS_5:41
.= s . (intpos 7) by A34, A20, AMI_3:10, SCMPDS_2:50 ;
then A35: (Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . (intpos 5) = s . (intpos 7) by SCMPDS_5:15;
A36: (IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)) . (intpos 2) = (Exec (((GBP,6) := ((intpos 2),0)),(IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)))) . (intpos 2) by SCMPDS_5:41
.= md by A11, A14, AMI_3:10, SCMPDS_2:47 ;
(IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s)) . (intpos 2) = (Exec ((SubFrom (GBP,6,(intpos 3),0)),(IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)))) . (intpos 2) by SCMPDS_5:41
.= md by A36, A20, AMI_3:10, SCMPDS_2:50 ;
then A37: (Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . (intpos 2) = s . (intpos 2) by A1, SCMPDS_5:15;
intpos 4 <> DataLoc (((Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . GBP),3) by A30, AMI_3:10, SCMP_GCD:1;
then A38: (Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 4) = s . (intpos 4) by A28, SCMPDS_2:48;
intpos 2 <> DataLoc (((Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . GBP),3) by A30, AMI_3:10, SCMP_GCD:1;
then A39: (Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 2) = s . (intpos 2) by A37, SCMPDS_2:48;
GBP <> DataLoc (((Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . GBP),3) by A30, AMI_3:10, SCMP_GCD:1;
then A40: (Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . GBP = 0 by A30, SCMPDS_2:48;
then A41: DataLoc (((Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . GBP),5) = intpos (0 + 5) by SCMP_GCD:1;

A42: now :: thesis:

let i be Nat; :: thesis:
assume i >= 8 ; :: thesis:
then i > 5 by XXREAL_0:2;
hence (Exec (((GBP,5) := (GBP,7)),s)) . (intpos i) = s . (intpos i) by A7, AMI_3:10, SCMPDS_2:47; :: thesis:

end;

A43: now :: thesis:

let i be Nat; :: thesis:
assume A44: i >= 8 ; :: thesis:
then A45: i > 7 by XXREAL_0:2;
thus (IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)) . (intpos i) = (Exec ((AddTo (GBP,7,(- 1))),(Exec (((GBP,5) := (GBP,7)),s)))) . (intpos i) by SCMPDS_5:42
.= (Exec (((GBP,5) := (GBP,7)),s)) . (intpos i) by A9, A45, AMI_3:10, SCMPDS_2:48
.= s . (intpos i) by A42, A44 ; :: thesis:

end;

A46: now :: thesis:

let i be Nat; :: thesis:
assume A47: i >= 8 ; :: thesis:
then A48: i > 6 by XXREAL_0:2;
thus (IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)) . (intpos i) = (Exec (((GBP,6) := ((intpos 2),0)),(IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)))) . (intpos i) by SCMPDS_5:41
.= (IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)) . (intpos i) by A14, A48, AMI_3:10, SCMPDS_2:47
.= s . (intpos i) by A43, A47 ; :: thesis:

end;

A49: now :: thesis:

let i be Nat; :: thesis:
assume A50: i >= 8 ; :: thesis:
then A51: i > 6 by XXREAL_0:2;
thus (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s)) . (intpos i) = (Exec ((SubFrom (GBP,6,(intpos 3),0)),(IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)))) . (intpos i) by SCMPDS_5:41
.= (IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)) . (intpos i) by A20, A51, AMI_3:10, SCMPDS_2:50
.= s . (intpos i) by A46, A50 ; :: thesis:

end;

A52: (IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)) . (intpos 6) = (Exec (((GBP,6) := ((intpos 2),0)),(IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)))) . (intpos 6) by SCMPDS_5:41
.= (IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)) . (intpos md) by A14, A12, SCMPDS_2:47
.= s . (intpos md) by A3, A43 ;
(IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s)) . (intpos 6) = (Exec ((SubFrom (GBP,6,(intpos 3),0)),(IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)))) . (intpos 6) by SCMPDS_5:41
.= ((IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)) . (intpos 6)) - ((IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)) . (DataLoc (((IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)) . (intpos 3)),0))) by A20, SCMPDS_2:50
.= ((IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)) . (intpos 6)) - ((IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)) . (intpos (me + 0))) by A18, SCMP_GCD:1
.= (s . (intpos md)) - (s . (intpos me)) by A4, A52, A46 ;
then A53: (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s)) . (DataLoc (((IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s)) . GBP),6)) = (s . (intpos md)) - (s . (intpos me)) by A29, SCMP_GCD:1;
intpos 1 <> DataLoc (((Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . GBP),3) by A30, AMI_3:10, SCMP_GCD:1;
then A54: (Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 1) = s . (intpos 1) by A26, SCMPDS_2:48;

A55: now :: thesis:

per cases ) . (DataLoc (((Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . GBP),6)) <= 0 or (Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . (DataLoc (((Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . GBP),6)) > 0 ) ;

suppose A56: (Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . (DataLoc (((Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . GBP),6)) <= 0 ; :: thesis:

hence (IExec ((if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . GBP = (IExec ((Load ((GBP,7) := 0)),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . GBP by SCMPDS_6:74
.= (Exec (((GBP,7) := 0),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . GBP by SCMPDS_5:40
.= 0 by A30, A31, AMI_3:10, SCMPDS_2:46 ;
:: thesis:
thus (IExec ((if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 1) = (IExec ((Load ((GBP,7) := 0)),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 1) by A56, SCMPDS_6:74
.= (Exec (((GBP,7) := 0),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 1) by SCMPDS_5:40
.= s . (intpos 1) by A26, A31, AMI_3:10, SCMPDS_2:46 ; :: thesis:
thus (IExec ((if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 2) = (IExec ((Load ((GBP,7) := 0)),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 2) by A56, SCMPDS_6:74
.= (Exec (((GBP,7) := 0),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 2) by SCMPDS_5:40
.= s . (intpos 2) by A37, A31, AMI_3:10, SCMPDS_2:46 ; :: thesis:
thus (IExec ((if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 4) = (IExec ((Load ((GBP,7) := 0)),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 4) by A56, SCMPDS_6:74
.= (Exec (((GBP,7) := 0),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 4) by SCMPDS_5:40
.= s . (intpos 4) by A28, A31, AMI_3:10, SCMPDS_2:46 ; :: thesis:
let i be Nat; :: thesis:
assume A57: i >= 8 ; :: thesis:
then A58: i > 7 by XXREAL_0:2;
thus (IExec (((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))) ';' (if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0))))),P,s)) . (intpos i) = (IExec ((if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos i) by SCMPDS_5:35
.= (IExec ((Load ((GBP,7) := 0)),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos i) by A56, SCMPDS_6:74
.= (Exec (((GBP,7) := 0),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos i) by SCMPDS_5:40
.= (Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . (intpos i) by A31, A58, AMI_3:10, SCMPDS_2:46
.= (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s)) . (intpos i) by SCMPDS_5:15
.= s . (intpos i) by A49, A57 ; :: thesis:

end;

suppose A59: (Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . (DataLoc (((Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . GBP),6)) > 0 ; :: thesis:

hence (IExec ((if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . GBP = (IExec (((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . GBP by SCMPDS_6:73
.= (Exec ((AddTo (GBP,5,(- 1))),(Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))))) . GBP by SCMPDS_5:42
.= 0 by A40, A41, AMI_3:10, SCMPDS_2:48 ;
:: thesis:
thus (IExec ((if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 1) = (IExec (((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 1) by A59, SCMPDS_6:73
.= (Exec ((AddTo (GBP,5,(- 1))),(Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))))) . (intpos 1) by SCMPDS_5:42
.= s . (intpos 1) by A54, A41, AMI_3:10, SCMPDS_2:48 ; :: thesis:
thus (IExec ((if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 2) = (IExec (((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 2) by A59, SCMPDS_6:73
.= (Exec ((AddTo (GBP,5,(- 1))),(Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))))) . (intpos 2) by SCMPDS_5:42
.= s . (intpos 2) by A39, A41, AMI_3:10, SCMPDS_2:48 ; :: thesis:
thus (IExec ((if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 4) = (IExec (((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 4) by A59, SCMPDS_6:73
.= (Exec ((AddTo (GBP,5,(- 1))),(Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))))) . (intpos 4) by SCMPDS_5:42
.= s . (intpos 4) by A38, A41, AMI_3:10, SCMPDS_2:48 ; :: thesis:
let i be Nat; :: thesis:
assume A60: i >= 8 ; :: thesis:
then A61: i > 5 by XXREAL_0:2;
i > 3 by A60, XXREAL_0:2;
then A62: intpos i <> DataLoc (((Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . GBP),3) by A30, AMI_3:10, SCMP_GCD:1;
thus (IExec (((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))) ';' (if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0))))),P,s)) . (intpos i) = (IExec ((if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos i) by SCMPDS_5:35
.= (IExec (((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos i) by A59, SCMPDS_6:73
.= (Exec ((AddTo (GBP,5,(- 1))),(Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))))) . (intpos i) by SCMPDS_5:42
.= (Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos i) by A41, A61, AMI_3:10, SCMPDS_2:48
.= (Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . (intpos i) by A62, SCMPDS_2:48
.= (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s)) . (intpos i) by SCMPDS_5:15
.= s . (intpos i) by A49, A60 ; :: thesis:

end;

hence ( (IExec (((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))) ';' (if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0))))),P,s)) . GBP = 0 & (IExec (((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))) ';' (if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0))))),P,s)) . (intpos 1) = s . (intpos 1) & (IExec (((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))) ';' (if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0))))),P,s)) . (intpos 2) = s . (intpos 2) & (IExec (((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))) ';' (if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0))))),P,s)) . (intpos 4) = s . (intpos 4) ) by SCMPDS_5:35; :: thesis:
thus for i being Nat st i >= 8 holds
(IExec (((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))) ';' (if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0))))),P,s)) . (intpos i) = s . (intpos i) by A55; :: thesis:
A63: (IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)) . (intpos 7) = (Exec ((AddTo (GBP,7,(- 1))),(Exec (((GBP,5) := (GBP,7)),s)))) . (intpos 7) by SCMPDS_5:42
.= ((Exec (((GBP,5) := (GBP,7)),s)) . (intpos 7)) + (- 1) by A9, SCMPDS_2:48
.= (s . (intpos 7)) - 1 by A17 ;
A64: (IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)) . (intpos 7) = (Exec (((GBP,6) := ((intpos 2),0)),(IExec ((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))),P,s)))) . (intpos 7) by SCMPDS_5:41
.= (s . (intpos 7)) - 1 by A63, A14, AMI_3:10, SCMPDS_2:47 ;
(IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s)) . (intpos 7) = (Exec ((SubFrom (GBP,6,(intpos 3),0)),(IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)))) . (intpos 7) by SCMPDS_5:41
.= (s . (intpos 7)) - 1 by A64, A20, AMI_3:10, SCMPDS_2:50 ;
then A65: (Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . (intpos 7) = (s . (intpos 7)) - 1 by SCMPDS_5:15;
(IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s)) . (intpos 3) = (Exec ((SubFrom (GBP,6,(intpos 3),0)),(IExec (((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))),P,s)))) . (intpos 3) by SCMPDS_5:41
.= me by A18, A20, AMI_3:10, SCMPDS_2:50 ;
then A66: (Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . (intpos 3) = s . (intpos 3) by A2, SCMPDS_5:15;
A67: DataLoc (((Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . GBP),3) = intpos (0 + 3) by A30, SCMP_GCD:1;
A68: (Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . (DataLoc (((Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . GBP),6)) = (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s)) . (DataLoc (((Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . GBP),6)) by SCMPDS_5:15
.= (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s)) . (DataLoc (((IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s)) . GBP),6)) by SCMPDS_5:15 ;

hereby :: thesis:

A69: intpos 7 <> DataLoc (((Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . GBP),3) by A30, AMI_3:10, SCMP_GCD:1;
assume s . (intpos md) > s . (intpos me) ; :: thesis:
then A70: (s . (intpos md)) - (s . (intpos me)) > 0 by XREAL_1:50;
thus (IExec (((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))) ';' (if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0))))),P,s)) . (intpos 7) = (IExec ((if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 7) by SCMPDS_5:35
.= (IExec (((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 7) by A53, A68, A70, SCMPDS_6:73
.= (Exec ((AddTo (GBP,5,(- 1))),(Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))))) . (intpos 7) by SCMPDS_5:42
.= (Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 7) by A41, AMI_3:10, SCMPDS_2:48
.= (s . (intpos 7)) - 1 by A65, A69, SCMPDS_2:48 ; :: thesis:
thus (IExec (((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))) ';' (if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0))))),P,s)) . (intpos 3) = (IExec ((if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 3) by SCMPDS_5:35
.= (IExec (((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 3) by A53, A68, A70, SCMPDS_6:73
.= (Exec ((AddTo (GBP,5,(- 1))),(Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))))) . (intpos 3) by SCMPDS_5:42
.= (Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 3) by A41, AMI_3:10, SCMPDS_2:48
.= (s . (intpos 3)) + 1 by A67, A66, SCMPDS_2:48 ; :: thesis:
A71: intpos 5 <> DataLoc (((Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))) . GBP),3) by A30, AMI_3:10, SCMP_GCD:1;
thus (IExec (((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))) ';' (if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0))))),P,s)) . (intpos 5) = (IExec ((if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 5) by SCMPDS_5:35
.= (IExec (((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 5) by A53, A68, A70, SCMPDS_6:73
.= (Exec ((AddTo (GBP,5,(- 1))),(Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))))) . (intpos 5) by SCMPDS_5:42
.= ((Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 5)) + (- 1) by A41, SCMPDS_2:48
.= ((Exec ((AddTo (GBP,3,1)),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 5)) - 1
.= (s . (intpos 7)) - 1 by A35, A71, SCMPDS_2:48 ; :: thesis:

end;

hereby :: thesis:

assume s . (intpos md) <= s . (intpos me) ; :: thesis:
then A72: 0 >= (s . (intpos md)) - (s . (intpos me)) by XREAL_1:47;
thus (IExec (((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))) ';' (if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0))))),P,s)) . (intpos 7) = (IExec ((if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 7) by SCMPDS_5:35
.= (IExec ((Load ((GBP,7) := 0)),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 7) by A53, A68, A72, SCMPDS_6:74
.= (Exec (((GBP,7) := 0),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 7) by SCMPDS_5:40
.= 0 by A31, SCMPDS_2:46 ; :: thesis:
thus (IExec (((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))) ';' (if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0))))),P,s)) . (intpos 3) = (IExec ((if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 3) by SCMPDS_5:35
.= (IExec ((Load ((GBP,7) := 0)),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 3) by A53, A68, A72, SCMPDS_6:74
.= (Exec (((GBP,7) := 0),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 3) by SCMPDS_5:40
.= s . (intpos 3) by A31, A66, AMI_3:10, SCMPDS_2:46 ; :: thesis:
thus (IExec (((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))) ';' (if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0))))),P,s)) . (intpos 5) = (IExec ((if>0 (GBP,6,((AddTo (GBP,3,1)) ';' (AddTo (GBP,5,(- 1)))),(Load ((GBP,7) := 0)))),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 5) by SCMPDS_5:35
.= (IExec ((Load ((GBP,7) := 0)),P,(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 5) by A53, A68, A72, SCMPDS_6:74
.= (Exec (((GBP,7) := 0),(Initialize (IExec ((((((GBP,5) := (GBP,7)) ';' (AddTo (GBP,7,(- 1)))) ';' ((GBP,6) := ((intpos 2),0))) ';' (SubFrom (GBP,6,(intpos 3),0))),P,s))))) . (intpos 5) by SCMPDS_5:40
.= s . (intpos 7) by A35, A31, AMI_3:10, SCMPDS_2:46 ; :: thesis:

end;