Nuprl - Pf total_back_listify 1 1 2 2 1 2 1

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. AL: S.car*
13. s:S.car. False (w:Alph*. mem_f(S.car;(S:ws);sL))
14. s:S.car. mem_f(S.car;s;sL) mem_f(S.car;s;TBL) False
15. s:S.car, a:Alph. mem_f(S.car;S.act(a,s);TBL) mem_f(S.car;s;TBL) False
16. s: S.car
17. w: Alph*
18. mem_f(S.car;(S:ws);sL)

i:. i||w|| mem_f(S.car;(S:nth_tl(i;w)s);TBL)

By: Analyze 0 THEN NatInd -1 THEN RepD

Generated subgoals:

1 19. 0||w||
mem_f(S.car;(S:nth_tl(0;w)s);TBL)

2 19. i:
20. 0 < i
21. i-1||w|| mem_f(S.car;(S:nth_tl(i-1;w)s);TBL)
22. i||w||
mem_f(S.car;(S:nth_tl(i;w)s);TBL)

About:

1	19. `0\|\|w\|\|` `mem_f(S.car;(S:nth_tl(0;w)s);TBL)`
2	19. `i:` 20. `0 < i` 21. `i-1\|\|w\|\| mem_f(S.car;(S:nth_tl(i-1;w)s);TBL)` 22. `i\|\|w\|\|` `mem_f(S.car;(S:nth_tl(i;w)s);TBL)`