Nuprl - Pf mn_23_lem_1 1 1 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. x: x,y:Alph*//(x R y)
9. y: x,y:Alph*//(x R y)

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

By: Assert ( < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)),a,p. p/x,y. < a.x,a.y > > ActionSet(Alph))

Generated subgoals:

1 < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)),a,p. p/x,y. < a.x,a.y > > ActionSet(Alph)

2 10. < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)),a,p. p/x,y. < a.x,a.y > > ActionSet(Alph)
Dec(x@0:Alph*. (g(x@0@x)) = (g(x@0@y)) = false)

About:

1	`< (x,y:Alph//(x R y))(x,y:Alph//(x R y)),a,p. p/x,y. < a.x,a.y > > ActionSet(Alph)`
2	10. `< (x,y:Alph//(x R y))(x,y:Alph//(x R y)),a,p. p/x,y. < a.x,a.y > > ActionSet(Alph)` `Dec(x@0:Alph*. (g(x@0@x)) = (g(x@0@y)) = false)`