Nuprl - Pf total_back_listify 1 1 2 2 2 2 3 1 1 1 2

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At: total back listify 1 1 2 2 2 2 3 1 1 1 2

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)
18. BL: S.car*
19. t:S.car. mem_f(S.car;t;BL) (a:Alph. S.act(a,t) = u)
20. s: S.car
21. mem_f(S.car;s;BL)
22. a: Alph
23. S.act(a,s) = u
24. w: Alph*
25. mem_f(S.car;(S:wS.act(a,s));sL)

w:Alph*. mem_f(S.car;(S:ws);sL)

By: InstConcl [w @ [a]] THEN RWH (LemmaC Thm* S:ActionSet(T), s:S.car, tl1,tl2:T*. (S:tl1 @ tl2s) = (S:tl1(S:tl2s))) 0

Generated subgoal:

1 mem_f(S.car;(S:w(S:[a]s));sL)

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