Nuprl - Pf mn_23_lem

PrintForm Definitions myhill nerode Sections AutomataTheory Doc

1. Alph: Type
2. R: Alph*Alph*Prop
3. Fin(Alph)
4. EquivRel x,y:Alph*. x R y
5. Fin(x,y:Alph*//(x R y))
6. x,y,z:Alph*. (x R y) ((z @ x) R (z @ y))
7. g: (x,y:Alph*//(x R y))
8. x: x,y:Alph*//(x R y)
9. y: x,y:Alph*//(x R y)

Dec(z:Alph*. g(z@x) = g(z@y))

By: Inst Thm* P:(TProp). (x:T. Dec(P(x))) & Dec(x:T. P(x)) Dec(x:T. P(x)) [Alph*;z.g(z@x) = g(z@y)]

Generated subgoals:

1 10. x@0: Alph*
Dec((z.g(z@x) = g(z@y))(x@0))

2 Dec(x@0:Alph*. (z.g(z@x) = g(z@y))(x@0))

3 10. Dec(x@0:Alph*. (z.g(z@x) = g(z@y))(x@0))
Dec(z:Alph*. g(z@x) = g(z@y))

About:

1	10. `x@0:` `Alph*` `Dec((z.g(z@x) = g(z@y))(x@0))`
2	`Dec(x@0:Alph*. (z.g(z@x) = g(z@y))(x@0))`
3	10. `Dec(x@0:Alph. (z.g(z@x) = g(z@y))(x@0))` `Dec(z:Alph. g(z@x) = g(z@y))`