Nuprl - Proof: paren interval 3 1 1

(60steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc

1. T: Type
2. s: (T+T) List
3. t: T
4. no_repeats(T+T;s) (s1,s2,s3:(T+T) List, x:T. s = (s1 @ [inl(x) / (s2 @ [inr(x) / s3])]) paren(T;s2))
5. paren(T;s)
6. l_disjoint(T+T;[inl(t)];s @ [inr(t)])
7. no_repeats(T+T;[inl(t)])
8. l_disjoint(T+T;s;[inr(t)])
9. no_repeats(T+T;s)
10. no_repeats(T+T;[inr(t)])
11. s2: (T+T) List
12. s3: (T+T) List
13. x: T
14. inl(t) = inl(x) T+T
15. (s @ [inr(t)]) = (s2 @ [inr(x) / s3])

paren(T;s2)

By: EqualAppendsD -1 THEN Analyze -1

Generated subgoals:

1 16. e: (T+T) List
17. s = (s2 @ e)
18. [inr(x) / s3] = (e @ [inr(t)])
paren(T;s2) 5 steps

2 16. e: (T+T) List
17. s2 = (s @ e)
18. [inr(t)] = (e @ [inr(x) / s3])
paren(T;s2) 3 steps

About:

(60steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc

1	16. `e:` `(T+T) List` 17. `s = (s2 @ e)` 18. `[inr(x) / s3] = (e @ [inr(t)])` `paren(T;s2)`	5 steps

2	16. `e:` `(T+T) List` 17. `s2 = (s @ e)` 18. `[inr(t)] = (e @ [inr(x) / s3])` `paren(T;s2)`	3 steps