let s be State of SCM+FSA; :: thesis: 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; :: thesis: 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; :: thesis: 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 ; :: thesis: ( ( 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 ) ; :: thesis: ((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 ; :: thesis: verum