At: pump theorem11111111111211 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 & f o g = Id 8. A: Alph* 9. N < ||A|| 10. i: ||A|| 11. j: ||A|| 12. i < j 13. (i.f((S:A[||A||-i..||A||]s)))(i) = (i.f((S:A[||A||-i..||A||]s)))(j) N
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. (i.f((S:A[||A||-i..||A||]s)))(i) = (i.f((S:A[||A||-i..||A||]s)))(j) N k:. (S:((A[0..||A||-j]) @ (A[||A||-j..||A||-i]k)) @ (A[||A||-i..||A||])s) = (S:As)