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

At: paren interval 3 1 2 1 2 1 1 1
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. u: T+T
12. v: (T+T) List
13. s2: (T+T) List
14. s3: (T+T) List
15. x: T
16. inl(t) = u
17. (s @ [inr(t)]) = (v @ [inl(x) / (s2 @ [inr(x) / s3])])
18. u1: T+T
19. v1: (T+T) List
20. s = (v @ [inl(x) / v1])
21. (s2 @ [inr(x) / s3]) = (v1 @ [inr(t)])
22. e: (T+T) List
23. s2 = (v1 @ e)
24. [inr(t)] = (e @ [inr(x) / s3])
25. e = nil
26. inr(x) = inr(t) T+T
27. s3 = nil
paren(T;s2)
By:
Unfold `l_disjoint` 6
THEN
InstHyp [inl(x)] 6
THEN
Analyze -1
THEN
SubstFor s 0
Generated subgoal:

16. x:T+T. ((x [inl(t)]) & (x 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. u: T+T
12. v: (T+T) List
13. s2: (T+T) List
14. s3: (T+T) List
15. x: T
16. inl(t) = u
17. (s @ [inr(t)]) = (v @ [inl(x) / (s2 @ [inr(x) / s3])])
18. u1: T+T
19. v1: (T+T) List
20. s = (v @ [inl(x) / v1])
21. (s2 @ [inr(x) / s3]) = (v1 @ [inr(t)])
22. e: (T+T) List
23. s2 = (v1 @ e)
24. [inr(t)] = (e @ [inr(x) / s3])
25. e = nil
26. inr(x) = inr(t) T+T
27. s3 = nil
(inl(x) [inl(t)]) & (inl(x) (v @ [inl(x) / v1]) @ [inr(t)])		1 step

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listconsconsnilunioninl
inruniverseequalimpliesandall

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