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1. Alph: Type
2. S: ActionSet(Alph)
3. s: S.car
4. n:
5. f: nAlph
6. Bij(n; Alph; f)
7. n1:
8. f1: n1S.car
9. Bij(n1; S.car; f1)
10. BL: S.car*
11. t: S.car
12. a:Alph. S.act(a,t) = s
13. mem_f(S.car;t;BL) (i:||(x. < f1(x),(y.S.act(f(y),f1(x)))[n] > )[n1]||. f1(i) = t & mem_f(S.car;s;(y.S.act(f(y),f1(i)))[n]))
14. mem_f(S.car;t;BL) (i:||(x. < f1(x),(y.S.act(f(y),f1(x)))[n] > )[n1]||. f1(i) = t & mem_f(S.car;s;(y.S.act(f(y),f1(i)))[n]))

mem_f(S.car;t;BL)

By:
BackThru -1
THEN
Thin -1
THEN
Thin -1
THEN
Analyze -1


Generated subgoal:

112. a: Alph
13. S.act(a,t) = s
i:||(x. < f1(x),(y.S.act(f(y),f1(x)))[n] > )[n1]||. f1(i) = t & mem_f(S.car;s;(y.S.act(f(y),f1(i)))[n])


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