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At: total back listify 1 2 1 2
1. Alph: Type
2. S: ActionSet(Alph)
3. sL: S.car*
4. Fin(Alph)
5. n:
6. f: nS.car
7. g: S.carn
8. InvFuns(n; S.car; f; g)
9. n:. TBL:S.car*. (s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))) ||TBL|| = n & (i:||TBL||, j:i. TBL[i] = TBL[j]) & (s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))) & (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) mem_f(S.car;s;TBL) mem_f(S.car;s;AL)) & (s:S.car, a:Alph. mem_f(S.car;S.act(a,s);TBL) mem_f(S.car;s;TBL) mem_f(S.car;s;AL)))
10. n = 0

TBL:S.car*. s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))
By:
InstHyp [n+1] -2
THEN
Analyze -1
THEN
Analyze -1
THEN
ExRepD
Generated subgoals:

111. TBL: S.car*
12. s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))
TBL:S.car*. s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))
211. TBL: S.car*
12. ||TBL|| = n+1
13. i:||TBL||, j:i. TBL[i] = TBL[j]
14. s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))
15. AL: S.car*
16. s:S.car. mem_f(S.car;s;AL) (w:Alph*. mem_f(S.car;(S:ws);sL))
17. s:S.car. mem_f(S.car;s;sL) mem_f(S.car;s;TBL) mem_f(S.car;s;AL)
18. s:S.car, a:Alph. mem_f(S.car;S.act(a,s);TBL) mem_f(S.car;s;TBL) mem_f(S.car;s;AL)
TBL:S.car*. s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))

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