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At: paren balance2

T:Type, s':(T+T) List. paren(T;s') (i:T. (inr(i) s') (inl(i) s'))

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THEN
BackThru Thm* paren_induction


Generated subgoals:

11. T: Type
2. i: T
3. (inr(i) nil)
(inl(i) nil)
1 step
 
21. T: Type
2. s1: (T+T) List
3. s2: (T+T) List
4. i:T. (inr(i) s1) (inl(i) s1)
5. i:T. (inr(i) s2) (inl(i) s2)
6. paren(T;s1)
7. paren(T;s2)
8. i: T
9. (inr(i) s1 @ s2)
(inl(i) s1 @ s2)
2 steps
 
31. T: Type
2. s': (T+T) List
3. t: T
4. i:T. (inr(i) s') (inl(i) s')
5. paren(T;s')
6. i: T
7. (inr(i) [inl(t)] @ s' @ [inr(t)])
(inl(i) [inl(t)] @ s' @ [inr(t)])
1 step

About:
listconsnilunioninlinrfunctionuniversepropimpliesall

(5steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc