Nuprl - Pf n0n1_irregular 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1

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At: n0n1 irregular 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1

1. S: ActionSet()
2. s: S.car
3. q: S.car
4. n:
5. f: S.carn
6. g: nS.car
7. g o f = Id
8. f o g = Id
9. k:. (S:n0n1(k)s) = q
10. i: (n+1)
11. j: (n+1)
12. i < j
13. f((S:([1]i)s)) = f((S:([1]j)s))
14. (S:([1]i)s) = (S:([1]j)s)
15. k:
16. (([0]j) @ ([1]i)) = (([0]k) @ ([1]k))
17. k = i
18. j(1+||0:nil||)+i||0:nil|| = k(1+||0:nil||)+k||0:nil||
19. ||0:([0]j)||+||0:([1]i)||0

False

By: RWH (RecUnfoldC `el_counter`) 18

Generated subgoal:

1 18. j(1+if null(nil)0 ;0=hd(nil)1+||0:tl(nil)|| else ||0:tl(nil)|| fi) +iif null(nil)0 ;0=hd(nil)1+||0:tl(nil)|| else ||0:tl(nil)|| fi = k(1+if null(nil)0 ;0=hd(nil)1+||0:tl(nil)|| else ||0:tl(nil)|| fi) +kif null(nil)0 ;0=hd(nil)1+||0:tl(nil)|| else ||0:tl(nil)|| fi
19. ||0:([0]j)||+||0:([1]i)||0
False

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