PrintForm Definitions automata 5 Sections AutomataTheory Doc

At: homo is surj 1 1
1. Alph: Type
2. St: Type
3. Auto: Automata(Alph;St)
4. c: StAlph*
5. (q:St. (Result(Auto)c(q)) = q) & Fin(Alph) & Fin(St)
6. EquivRel x,y:Alph*. x LangOf(Auto)-induced Equiv y

Surj(St; x,y:Alph*//(x LangOf(Auto)-induced Equiv y); c)
By: Inst Thm* E:(Alph*Alph*Prop). Fin(Alph) & (EquivRel x,y:Alph*. x E y) & (x,y:Alph*. Dec(x E y)) (h:(Alph*Alph*). (x,y:Alph*. (x E y) h(x) = h(y)) & (x:Alph*. x E (h(x)))) [Alph;x,y. x = y]
Generated subgoals:

15. q:St. (Result(Auto)c(q)) = q
6. Fin(Alph)
7. Fin(St)
8. EquivRel x,y:Alph*. x LangOf(Auto)-induced Equiv y
EquivRel x,y:Alph*. x (x,y. x = y x,y:Alph*//(x LangOf(Auto)-induced Equiv y)) y
25. q:St. (Result(Auto)c(q)) = q
6. Fin(Alph)
7. Fin(St)
8. EquivRel x,y:Alph*. x LangOf(Auto)-induced Equiv y
9. x: Alph*
10. y: Alph*
Dec(x (x,y. x = y x,y:Alph*//(x LangOf(Auto)-induced Equiv y)) y)
37. h:(Alph*Alph*). (x,y:Alph*. (x (x,y. x = y x,y:Alph*//(x LangOf(Auto)-induced Equiv y)) y) h(x) = h(y)) & (x:Alph*. x (x,y. x = y x,y:Alph*//(x LangOf(Auto)-induced Equiv y)) (h(x)))
Surj(St; x,y:Alph*//(x LangOf(Auto)-induced Equiv y); c)

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