Nuprl - Pf sublist transitivity 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1

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At: sublist transitivity 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1

1. T: Type
2. Discrete{T}
3. eq: {T}
4. eq TT
5. x:T. eq(x,x)
6. x,y:T. eq(x,y) eq(y,x)
7. x,y,z:T. eq(x,y) eq(y,z) eq(x,z)
8. L1: T List
9. L2: T List
10. L3: T List
11. f: {T=}
12. f TT
13. x,y:T. f(x,y) x = y
14. z: T
15. z(f) L1
16. u: T
17. v: T List
18. (z:T. z(f) v z(eq) L3) z(eq) v z(eq) L3
19. eq(z,u) = true
20. True
21. if f(u,u) true else u(f) v fi u(eq) L3

f(u,u)

By: Witness13 u THEN With u (Analyze -1) THEN Analyze -1

Generated subgoal:

1 13. z: T
14. z(f) L1
15. u: T
16. v: T List
17. (z:T. z(f) v z(eq) L3) z(eq) v z(eq) L3
18. eq(z,u) = true
19. True
20. if f(u,u) true else u(f) v fi u(eq) L3
21. f(u,u) u = u
22. (f(u,u)) (u = u)
f(u,u)

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