Nuprl - Pf mn_23_lem 1 2 2 1 3 2

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. t:((x,y:Alph*//(x R y))(x,y:Alph*//(x R y))). (x.x/x1,x2.(g(x1)) = (g(x2)))(t) mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y));t;fL)
12. < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)),a,xy. xy/x,y. < a.x,a.y > > ActionSet(Alph)
13. TBL: < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)),a,xy. xy/x,y. < a.x,a.y > > .car*. s: < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)),a,xy. xy/x,y. < a.x,a.y > > .car. mem_f( < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)),a,xy. xy/x,y. < a.x,a.y > > .car;s;TBL) (w:Alph*. mem_f( < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)) ,a,xy. xy/x,y. < a.x,a.y > > .car;( < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)) ,a,xy. xy/x,y. < a.x,a.y > > :ws);fL))

x,y:x,y:Alph*//(x R y). Dec(x Rg y)

By: Unfold `aset_car` -1 THEN Reduce -1 THEN Reduce -2 THEN GenExRepD

Generated subgoal:

1 13. TBL: ((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)))*
14. s:((x,y:Alph*//(x R y))(x,y:Alph*//(x R y))). mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y));s;TBL) (w:Alph*. mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y));( < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)) ,a,xy. xy/x,y. < a.x,a.y > > :ws);fL))
15. x: x,y:Alph*//(x R y)
16. y: x,y:Alph*//(x R y)
Dec(x Rg y)

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