Nuprl - Pf Rl_quo_is_decidable 1 1 1 1 1 1

PrintForm Definitions automata 5 Sections AutomataTheory Doc

1. Alph: Type
2. St: Type
3. Auto: Automata(Alph;St)
4. Fin(Alph) & Fin(St)
5. x: Alph*
6. y: Alph*
7. n:
8. f: n(x,y:Alph*//(x LangOf(Auto)-induced Equiv y))
9. g: (x,y:Alph*//(x LangOf(Auto)-induced Equiv y))n
10. InvFuns(n; x,y:Alph*//(x LangOf(Auto)-induced Equiv y); f; g)
11. EquivRel x,y:Alph*. x LangOf(Auto)-induced Equiv y

Dec(x = y x,y:Alph*//(x LangOf(Auto)-induced Equiv y))

By: Assert (x = y g(x) = g(y))

Generated subgoals:

1 x = y x,y:Alph*//(x LangOf(Auto)-induced Equiv y) g(x) = g(y)

2 12. x = y x,y:Alph*//(x LangOf(Auto)-induced Equiv y) g(x) = g(y)
Dec(x = y x,y:Alph*//(x LangOf(Auto)-induced Equiv y))

About:

1	`x = y x,y:Alph*//(x LangOf(Auto)-induced Equiv y) g(x) = g(y)`
2	12. `x = y x,y:Alph//(x LangOf(Auto)-induced Equiv y) g(x) = g(y)` `Dec(x = y x,y:Alph//(x LangOf(Auto)-induced Equiv y))`