PrintForm Definitions automata 5 Sections AutomataTheory Doc

At: homo is surj 1 1 3 1 1 1 2 1 1 1 1
1. Alph: Type
2. St: Type
3. Auto: Automata(Alph;St)
4. c: StAlph*
5. Fin(Alph) & Fin(St)
6. EquivRel x,y:Alph*. x LangOf(Auto)-induced Equiv y
7. h: Alph*Alph*
8. (x,y:Alph*. x = y x,y:Alph*//(x LangOf(Auto)-induced Equiv y) h(x) = h(y)) & (x:Alph*. x = h(x) x,y:Alph*//(x LangOf(Auto)-induced Equiv y))
9. b1: Alph*
10. b2: Alph*
11. b1 LangOf(Auto)-induced Equiv b2
12. (Result(Auto)c(Result(Auto)h(b1))) = (Result(Auto)h(b1))

c(Result(Auto)h(b1)) = b2 x,y:Alph*//(x LangOf(Auto)-induced Equiv y)
By:
Analyze 8
THEN
InstHyp [b1;b2] 8
Generated subgoal:

18. x,y:Alph*. x = y x,y:Alph*//(x LangOf(Auto)-induced Equiv y) h(x) = h(y)
9. x:Alph*. x = h(x) x,y:Alph*//(x LangOf(Auto)-induced Equiv y)
10. b1: Alph*
11. b2: Alph*
12. b1 LangOf(Auto)-induced Equiv b2
13. (Result(Auto)c(Result(Auto)h(b1))) = (Result(Auto)h(b1))
14. b1 = b2 x,y:Alph*//(x LangOf(Auto)-induced Equiv y) h(b1) = h(b2)
c(Result(Auto)h(b1)) = b2 x,y:Alph*//(x LangOf(Auto)-induced Equiv y)

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