let s be State 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,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,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,s) . 0 ) . a = s . a )
set ST = StepTimes a,I,s;
set au = 1 -stRWNotIn ({a} \/ (UsedIntLoc I));
set Is = Initialize s;
a in {a} by TARSKI:def 1;
then a in {a} \/ (UsedIntLoc I) by XBOOLE_0:def 3;
then A1: 1 -stRWNotIn ({a} \/ (UsedIntLoc I)) <> a by SFMASTR1:21;
assume A2: ( s . (intloc 0 ) = 1 or not a is read-only ) ; :: thesis: ((StepTimes a,I,s) . 0 ) . a = s . a
A3: ( a = intloc 0 or not a is read-only ) by SF_MASTR:def 5;
thus ((StepTimes a,I,s) . 0 ) . a = (Exec ((1 -stRWNotIn ({a} \/ (UsedIntLoc I))) := a),(Initialize s)) . a by SCMFSA_9:def 5
.= (Initialize s) . a by A1, SCMFSA_2:89
.= s . a by A2, A3, SCMFSA6C:3 ; :: thesis: verum