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

(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))

By: Reduce 0 THEN Analyze 0

Generated subgoals:

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

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

About:

1	`x@0:Alph*. Dec(g(x@0@x) g(x@0@y))`
2	`Dec(x@0:Alph*. (g(x@0@x) g(x@0@y)))`