At: auto iso sym11114111 1. Alph: Type 2. S1: Type 3. S2: Type 4. A1: Automata(Alph;S1) 5. A2: Automata(Alph;S2) 6. f: S1S2 7. Bij(S1; S2; f) 8. s:S1, a:Alph. f(A1(s,a)) = A2(f(s),a) 9. f(InitialState(A1)) = InitialState(A2) 10. g: S2S1 11. g o f = Id 12. f o g = Id 13. s: S2 14. (FinalState(A1) o g)(s) = FinalState(A2)((f o g)(s))