Nuprl - Pf mn_23_lem 1 2 2 1 3 2 1 2 1 1

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. Fin((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)))
9. a:Alph, x:x,y:Alph*//(x R y). a.x x,y:Alph*//(x R y)
10. fL: ((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)))*
11. < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)),a,xy. xy/x,y. < a.x,a.y > > ActionSet(Alph)
12. TBL: ((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)))*
13. x: x,y:Alph*//(x R y)
14. y: x,y:Alph*//(x R y)
15. mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)); < x,y > ;TBL) (w:Alph*. (g(w@x)) = (g(w@y)))

Dec(x Rg y)

By: Unfold `lquo_rel` 0 THEN Reduce 0 THEN 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)] THEN Reduce -1 THEN Try (Complete Auto)

Generated subgoal:

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

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