PrintForm Definitions automata 5 Sections AutomataTheory Doc

At: min auto con 1 1 1
1. Alph: Type
2. St: Type
3. Auto: Automata(Alph;St)
4. Fin(Alph) & Fin(St)
5. EquivRel x,y:Alph*. x LangOf(Auto)-induced Equiv y
6. s: x,y:Alph*//(x LangOf(Auto)-induced Equiv y)

l:Alph*. (Result(MinAuto(Auto))l) = s
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:

14. Fin(Alph)
5. Fin(St)
6. EquivRel x,y:Alph*. x LangOf(Auto)-induced Equiv y
7. s: 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
24. Fin(Alph)
5. Fin(St)
6. EquivRel x,y:Alph*. x LangOf(Auto)-induced Equiv y
7. s: x,y:Alph*//(x LangOf(Auto)-induced Equiv y)
8. x: Alph*
9. 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)))
l:Alph*. (Result(MinAuto(Auto))l) = s

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