begin
set SA0 = Start-At (0,SCM+FSA);
begin
Lm1:
Macro (halt SCM+FSA) is parahalting
Lm2:
Macro (halt SCM+FSA) is keeping_0
begin
Lm3:
now for I being keeping_0 parahalting Program of SCM+FSA
for s being State of SCM+FSA
for P being Instruction-Sequence of SCM+FSA holds DataPart (Initialized (IExec (I,P,s))) = DataPart (IExec (I,P,s))
set IF =
Data-Locations ;
let I be
keeping_0 parahalting Program of
SCM+FSA;
for s being State of SCM+FSA
for P being Instruction-Sequence of SCM+FSA holds DataPart (Initialized (IExec (I,P,s))) = DataPart (IExec (I,P,s))let s be
State of
SCM+FSA;
for P being Instruction-Sequence of SCM+FSA holds DataPart (Initialized (IExec (I,P,s))) = DataPart (IExec (I,P,s))let P be
Instruction-Sequence of
SCM+FSA;
DataPart (Initialized (IExec (I,P,s))) = DataPart (IExec (I,P,s))set IE =
IExec (
I,
P,
s);
now ( dom (DataPart (Initialized (IExec (I,P,s)))) = (dom (IExec (I,P,s))) /\ (Data-Locations ) & ( for x being set st x in dom (DataPart (Initialized (IExec (I,P,s)))) holds
(DataPart (Initialized (IExec (I,P,s)))) . x = (IExec (I,P,s)) . x ) )
A1:
dom (Initialized (IExec (I,P,s))) = the
carrier of
SCM+FSA
by PARTFUN1:def 2;
A2:
the
carrier of
SCM+FSA = {(IC )} \/ (Data-Locations )
by STRUCT_0:4;
A3:
dom (IExec (I,P,s)) = the
carrier of
SCM+FSA
by PARTFUN1:def 2;
hence
dom (DataPart (Initialized (IExec (I,P,s)))) = (dom (IExec (I,P,s))) /\ (Data-Locations )
by A1, RELAT_1:61;
for x being set st x in dom (DataPart (Initialized (IExec (I,P,s)))) holds
(DataPart (Initialized (IExec (I,P,s)))) . b2 = (IExec (I,P,s)) . b2then A4:
dom (DataPart (Initialized (IExec (I,P,s)))) = Data-Locations
by A3, A2, XBOOLE_1:21;
let x be
set ;
( x in dom (DataPart (Initialized (IExec (I,P,s)))) implies (DataPart (Initialized (IExec (I,P,s)))) . b1 = (IExec (I,P,s)) . b1 )assume A5:
x in dom (DataPart (Initialized (IExec (I,P,s))))
;
(DataPart (Initialized (IExec (I,P,s)))) . b1 = (IExec (I,P,s)) . b1
per cases
( x in Int-Locations or x in FinSeq-Locations )
by A5, A4, SCMFSA_2:100, XBOOLE_0:def 3;
suppose
x in Int-Locations
;
(DataPart (Initialized (IExec (I,P,s)))) . b1 = (IExec (I,P,s)) . b1
then reconsider x9 =
x as
Int-Location by AMI_2:def 16;
per cases
( x9 is read-write or x9 is read-only )
;
suppose
x9 is
read-only
;
(DataPart (Initialized (IExec (I,P,s)))) . b1 = (IExec (I,P,s)) . b1
then A7:
x9 = intloc 0
by SCMFSA_M:def 2;
thus (DataPart (Initialized (IExec (I,P,s)))) . x =
(Initialized (IExec (I,P,s))) . x9
by A5, A4, FUNCT_1:49
.=
1
by A7, SCMFSA_M:9
.=
(IExec (I,P,s)) . x
by A7, SCMFSA6B:11
;
verum
end;
end;
end;
end;
end;
hence
DataPart (Initialized (IExec (I,P,s))) = DataPart (IExec (I,P,s))
by FUNCT_1:46;
verum
end;
begin