Nuprl - Pf pump_theorem 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1

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At: pump theorem 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1

1. Alph: Type
2. S: ActionSet(Alph)
3. N:
4. s: S.car
5. f: S.carN
6. g: NS.car
7. g o f = Id
8. f o g = Id
9. A: Alph*
10. N < ||A||
11. i: ||A||
12. j: ||A||
13. i < j
14. f((S:A[||A||-i..||A||]s)) = f((S:A[||A||-j..||A||]s))
15. g(f((S:A[||A||-i..||A||]s))) = g(f((S:A[||A||-j..||A||]s)))

k:. (S:((A[0..||A||-j]) @ (A[||A||-j..||A||-i]k)) @ (A[||A||-i..||A||])s) = (S:As)

By: RW (SweepDnC add_composeC) 15

Generated subgoal:

1 15. (g o f)((S:A[||A||-i..||A||]s)) = (g o f)((S:A[||A||-j..||A||]s))
k:. (S:((A[0..||A||-j]) @ (A[||A||-j..||A||-i]k)) @ (A[||A||-i..||A||])s) = (S:As)

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