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 . () = 1 holds
((StepTimes (a,I,p,s)) . 0) | () = s | ()

let p be Instruction-Sequence of SCM+FSA; :: thesis: for a being Int-Location
for I being MacroInstruction of SCM+FSA st s . () = 1 holds
((StepTimes (a,I,p,s)) . 0) | () = s | ()

let a be Int-Location; :: thesis: for I being MacroInstruction of SCM+FSA st s . () = 1 holds
((StepTimes (a,I,p,s)) . 0) | () = s | ()

let I be MacroInstruction of SCM+FSA ; :: thesis: ( s . () = 1 implies ((StepTimes (a,I,p,s)) . 0) | () = s | () )
set ST = StepTimes (a,I,p,s);
set au = 1 -stRWNotIn ({a} \/ ());
set Is = Initialized s;
set UILI = UsedILoc I;
assume s . () = 1 ; :: thesis: ((StepTimes (a,I,p,s)) . 0) | () = s | ()
then A1: DataPart () = DataPart s by SCMFSA_M:19;
A2: now :: thesis: for x being Int-Location st x in UsedILoc I holds
((StepTimes (a,I,p,s)) . 0) . x = s . x
let x be Int-Location; :: thesis: ( x in UsedILoc I implies ((StepTimes (a,I,p,s)) . 0) . x = s . x )
A3: not 1 -stRWNotIn ({a} \/ ()) in {a} \/ () by SCMFSA_M:25;
assume x in UsedILoc I ; :: thesis: ((StepTimes (a,I,p,s)) . 0) . x = s . x
then A4: 1 -stRWNotIn ({a} \/ ()) <> x by ;
thus ((StepTimes (a,I,p,s)) . 0) . x = (Exec (((1 -stRWNotIn ({a} \/ ())) := a),())) . x by SCMFSA_9:def 5
.= () . x by
.= s . x by ; :: thesis: verum
end;
now :: thesis: for x being FinSeq-Location holds ((StepTimes (a,I,p,s)) . 0) . x = s . x
let x be FinSeq-Location ; :: thesis: ((StepTimes (a,I,p,s)) . 0) . x = s . x
thus ((StepTimes (a,I,p,s)) . 0) . x = (Exec (((1 -stRWNotIn ({a} \/ ())) := a),())) . x by SCMFSA_9:def 5
.= () . x by SCMFSA_2:63
.= s . x by SCMFSA_M:37 ; :: thesis: verum
end;
hence ((StepTimes (a,I,p,s)) . 0) | () = s | () by ; :: thesis: verum