let s be State of SCM+FSA; :: thesis: for p being Instruction-Sequence of SCM+FSA
for a being Int-Location
for I being Program of SCM+FSA st ( s . (intloc 0) = 1 or not a is read-only ) 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 Program of SCM+FSA st ( s . (intloc 0) = 1 or not a is read-only ) holds
((StepTimes (a,I,p,s)) . 0) . a = s . a
let a be Int-Location ; :: thesis: for I being Program of SCM+FSA st ( s . (intloc 0) = 1 or not a is read-only ) holds
((StepTimes (a,I,p,s)) . 0) . a = s . a
let I be Program of SCM+FSA; :: thesis: ( ( s . (intloc 0) = 1 or not a is read-only ) implies ((StepTimes (a,I,p,s)) . 0) . a = s . a )
set ST = StepTimes (a,I,p,s);
set au = 1 -stRWNotIn ({a} \/ (UsedIntLoc I));
set Is = Initialized s;
assume A1: ( s . (intloc 0) = 1 or not a is read-only ) ; :: thesis: ((StepTimes (a,I,p,s)) . 0) . a = s . a
A2: ( a = intloc 0 or not a is read-only ) by SF_MASTR:def 5;
a in {a} by TARSKI:def 1;
then a in {a} \/ (UsedIntLoc I) by XBOOLE_0:def 3;
then A3: 1 -stRWNotIn ({a} \/ (UsedIntLoc I)) <> a by SFMASTR1:20;
thus ((StepTimes (a,I,p,s)) . 0) . a = (Exec (((1 -stRWNotIn ({a} \/ (UsedIntLoc I))) := a),(Initialized s))) . a by SCMFSA_9:def 5
.= (Initialized s) . a by A3, SCMFSA_2:63
.= s . a by A1, A2, SCMFSA6A:38, SCMFSA6C:3 ; :: thesis: verum