Nuprl - Pf total_back_listify 1 1 2 2 2 2 3

PrintForm Definitions myhill nerode Sections AutomataTheory Doc

1. Alph: Type
2. S: ActionSet(Alph)
3. sL: S.car*
4. Fin(Alph)
5. Fin(S.car)
6. n:
7. 0 < n
8. TBL: S.car*
9. ||TBL|| = n-1
10. i:||TBL||, j:i. TBL[i] = TBL[j]
11. s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))
12. u: S.car
13. v: S.car*
14. s:S.car. u = s mem_f(S.car;s;v) (w:Alph*. mem_f(S.car;(S:ws);sL))
15. s:S.car. mem_f(S.car;s;sL) mem_f(S.car;s;TBL) u = s mem_f(S.car;s;v)
16. s:S.car, a:Alph. mem_f(S.car;S.act(a,s);TBL) mem_f(S.car;s;TBL) u = s mem_f(S.car;s;v)
17. mem_f(S.car;u;TBL)

AL:S.car*. (s:S.car. mem_f(S.car;s;AL) (w:Alph*. mem_f(S.car;(S:ws);sL))) & (s:S.car. mem_f(S.car;s;sL) u = s mem_f(S.car;s;TBL) mem_f(S.car;s;AL)) & (s:S.car, a:Alph. u = S.act(a,s) mem_f(S.car;S.act(a,s);TBL) u = s mem_f(S.car;s;TBL) mem_f(S.car;s;AL))

By: Inst Thm* S:ActionSet(Alph), s:S.car. Fin(Alph) Fin(S.car) (BL:S.car*. t:S.car. mem_f(S.car;t;BL) (a:Alph. S.act(a,t) = s)) [Alph;S;u] THEN Analyze -1

Generated subgoal:

1 18. BL: S.car*
19. t:S.car. mem_f(S.car;t;BL) (a:Alph. S.act(a,t) = u)
AL:S.car*. (s:S.car. mem_f(S.car;s;AL) (w:Alph*. mem_f(S.car;(S:ws);sL))) & (s:S.car. mem_f(S.car;s;sL) u = s mem_f(S.car;s;TBL) mem_f(S.car;s;AL)) & (s:S.car, a:Alph. u = S.act(a,s) mem_f(S.car;S.act(a,s);TBL) u = s mem_f(S.car;s;TBL) mem_f(S.car;s;AL))

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