let s be State of SCM+FSA; for p being Instruction-Sequence of SCM+FSA
for a being Int-Location
for I being MacroInstruction of SCM+FSA st ( s . (intloc 0) = 1 or a is read-write ) holds
((StepTimes (a,I,p,s)) . 0) . a = s . a
let p be Instruction-Sequence of SCM+FSA; for a being Int-Location
for I being MacroInstruction of SCM+FSA st ( s . (intloc 0) = 1 or a is read-write ) holds
((StepTimes (a,I,p,s)) . 0) . a = s . a
let a be Int-Location; for I being MacroInstruction of SCM+FSA st ( s . (intloc 0) = 1 or a is read-write ) holds
((StepTimes (a,I,p,s)) . 0) . a = s . a
let I be MacroInstruction of SCM+FSA ; ( ( s . (intloc 0) = 1 or a is read-write ) implies ((StepTimes (a,I,p,s)) . 0) . a = s . a )
set ST = StepTimes (a,I,p,s);
set au = 1 -stRWNotIn ({a} \/ (UsedILoc I));
set Is = Initialized s;
assume A1:
( s . (intloc 0) = 1 or a is read-write )
; ((StepTimes (a,I,p,s)) . 0) . a = s . a
A2:
( a = intloc 0 or a is read-write )
by SCMFSA_M:def 2;
a in {a}
by TARSKI:def 1;
then
a in {a} \/ (UsedILoc I)
by XBOOLE_0:def 3;
then A3:
1 -stRWNotIn ({a} \/ (UsedILoc I)) <> a
by SCMFSA_M:25;
thus ((StepTimes (a,I,p,s)) . 0) . a =
(Exec (((1 -stRWNotIn ({a} \/ (UsedILoc I))) := a),(Initialized s))) . a
by SCMFSA_9:def 5
.=
(Initialized s) . a
by A3, SCMFSA_2:63
.=
s . a
by A1, A2, SCMFSA_M:9, SCMFSA_M:37
; verum