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

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At: sublist transitivity 1 1 1 1 1 1 1 1 1 1 2 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. z:T. z(f) (u.v) z(eq) L3

if eq(z,u) true else z(eq) v fi z(eq) L3

By: GenConcl (eq(z,u) = b) THEN BoolInd -2 THEN Rewrite (HigherC ifthenelse_evalC THENC TryC (HigherC assert_evalC)) 0 THENL [Auto;Analyze 0]

Generated subgoals:

1 20. eq(z,u) = true
21. True
z(eq) L3

2 20. eq(z,u) = false
21. z(eq) v
z(eq) L3

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