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|---|---|---|---|---|---|---|---|---|
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Not_Not_intro | [194, 1] | [199, 13] | intro ha hna | a : Prop
⊢ a → ¬¬a | a : Prop
ha : a
hna : ¬a
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Not_Not_intro | [194, 1] | [199, 13] | apply hna | a : Prop
ha : a
hna : ¬a
⊢ False | a : Prop
ha : a
hna : ¬a
⊢ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Not_Not_intro | [194, 1] | [199, 13] | exact ha | a : Prop
ha : a
hna : ¬a
⊢ a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Exists_double_iden | [207, 1] | [211, 8] | apply Exists.intro 0 | ⊢ ∃ n, double n = n | ⊢ double 0 = 0 |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Exists_double_iden | [207, 1] | [211, 8] | rfl | ⊢ double 0 = 0 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.α_example | [238, 1] | [240, 9] | rfl | α β : Type
f : α → β
⊢ (fun x => f x) = fun y => f y | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.β_example | [243, 1] | [245, 9] | rfl | α β : Type
f : α → β
a : α
⊢ (fun x => f x) a = f a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.δ_example | [249, 1] | [251, 9] | rfl | ⊢ double 5 = 5 + 5 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.ζ_example | [256, 1] | [259, 9] | rfl | ⊢ (let n := 2;
n + n) =
4 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.η_example | [261, 1] | [263, 9] | rfl | α β : Type
f : α → β
⊢ (fun x => f x) = f | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.ι_example | [273, 1] | [275, 9] | rfl | α β : Type
a : α
b : β
⊢ myProd.first (myProd.mk a b) = a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Eq_trans_symm | [298, 1] | [305, 18] | apply Eq.trans | α : Type
a b c : α
hab : a = b
hcb : c = b
⊢ a = c | case h₁
α : Type
a b c : α
hab : a = b
hcb : c = b
⊢ a = ?b
case h₂
α : Type
a b c : α
hab : a = b
hcb : c = b
⊢ ?b = c
case b
α : Type
a b c : α
hab : a = b
hcb : c = b
⊢ α |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Eq_trans_symm | [298, 1] | [305, 18] | { exact hab } | case h₁
α : Type
a b c : α
hab : a = b
hcb : c = b
⊢ a = ?b
case h₂
α : Type
a b c : α
hab : a = b
hcb : c = b
⊢ ?b = c
case b
α : Type
a b c : α
hab : a = b
hcb : c = b
⊢ α | case h₂
α : Type
a b c : α
hab : a = b
hcb : c = b
⊢ b = c |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Eq_trans_symm | [298, 1] | [305, 18] | { apply Eq.symm
exact hcb } | case h₂
α : Type
a b c : α
hab : a = b
hcb : c = b
⊢ b = c | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Eq_trans_symm | [298, 1] | [305, 18] | exact hab | case h₁
α : Type
a b c : α
hab : a = b
hcb : c = b
⊢ a = ?b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Eq_trans_symm | [298, 1] | [305, 18] | apply Eq.symm | case h₂
α : Type
a b c : α
hab : a = b
hcb : c = b
⊢ b = c | case h₂.h
α : Type
a b c : α
hab : a = b
hcb : c = b
⊢ c = b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Eq_trans_symm | [298, 1] | [305, 18] | exact hcb | case h₂.h
α : Type
a b c : α
hab : a = b
hcb : c = b
⊢ c = b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Eq_trans_symm_rw | [312, 1] | [317, 13] | rw [hab] | α : Type
a b c : α
hab : a = b
hcb : c = b
⊢ a = c | α : Type
a b c : α
hab : a = b
hcb : c = b
⊢ b = c |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Eq_trans_symm_rw | [312, 1] | [317, 13] | rw [hcb] | α : Type
a b c : α
hab : a = b
hcb : c = b
⊢ b = c | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.a_proof_of_negation | [323, 1] | [331, 13] | rw [Not] | a : Prop
⊢ a → ¬¬a | a : Prop
⊢ a → ¬a → False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.a_proof_of_negation | [323, 1] | [331, 13] | rw [Not] | a : Prop
⊢ a → ¬a → False | a : Prop
⊢ a → (a → False) → False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.a_proof_of_negation | [323, 1] | [331, 13] | intro ha | a : Prop
⊢ a → (a → False) → False | a : Prop
ha : a
⊢ (a → False) → False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.a_proof_of_negation | [323, 1] | [331, 13] | intro hna | a : Prop
ha : a
⊢ (a → False) → False | a : Prop
ha : a
hna : a → False
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.a_proof_of_negation | [323, 1] | [331, 13] | apply hna | a : Prop
ha : a
hna : a → False
⊢ False | a : Prop
ha : a
hna : a → False
⊢ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.a_proof_of_negation | [323, 1] | [331, 13] | exact ha | a : Prop
ha : a
hna : a → False
⊢ a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.cong_two_args_1p1 | [339, 1] | [342, 21] | simp [hab, hcd] | α : Type
a b c d : α
g : α → α → ℕ → α
hab : a = b
hcd : c = d
⊢ g a c (1 + 1) = g b d 2 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.abc_Eq_cba | [348, 1] | [350, 12] | ac_rfl | a b c : ℕ
⊢ a + b + c = c + b + a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.add_zero | [359, 1] | [364, 35] | induction n with
| zero => rfl
| succ n' ih => simp [add, ih] | n : ℕ
⊢ add 0 n = n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.add_zero | [359, 1] | [364, 35] | rfl | case zero
⊢ add 0 Nat.zero = Nat.zero | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.add_zero | [359, 1] | [364, 35] | simp [add, ih] | case succ
n' : ℕ
ih : add 0 n' = n'
⊢ add 0 (Nat.succ n') = Nat.succ n' | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.add_succ | [368, 1] | [373, 35] | induction n with
| zero => rfl
| succ n' ih => simp [add, ih] | m n : ℕ
⊢ add (Nat.succ m) n = Nat.succ (add m n) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.add_succ | [368, 1] | [373, 35] | rfl | case zero
m : ℕ
⊢ add (Nat.succ m) Nat.zero = Nat.succ (add m Nat.zero) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.add_succ | [368, 1] | [373, 35] | simp [add, ih] | case succ
m n' : ℕ
ih : add (Nat.succ m) n' = Nat.succ (add m n')
⊢ add (Nat.succ m) (Nat.succ n') = Nat.succ (add m (Nat.succ n')) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.add_comm | [377, 1] | [382, 45] | induction n with
| zero => simp [add, add_zero]
| succ n' ih => simp [add, add_succ, ih] | m n : ℕ
⊢ add m n = add n m | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.add_comm | [377, 1] | [382, 45] | simp [add, add_zero] | case zero
m : ℕ
⊢ add m Nat.zero = add Nat.zero m | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.add_comm | [377, 1] | [382, 45] | simp [add, add_succ, ih] | case succ
m n' : ℕ
ih : add m n' = add n' m
⊢ add m (Nat.succ n') = add (Nat.succ n') m | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.add_assoc | [386, 1] | [391, 35] | induction n with
| zero => rfl
| succ n' ih => simp [add, ih] | l m n : ℕ
⊢ add (add l m) n = add l (add m n) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.add_assoc | [386, 1] | [391, 35] | rfl | case zero
l m : ℕ
⊢ add (add l m) Nat.zero = add l (add m Nat.zero) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.add_assoc | [386, 1] | [391, 35] | simp [add, ih] | case succ
l m n' : ℕ
ih : add (add l m) n' = add l (add m n')
⊢ add (add l m) (Nat.succ n') = add l (add m (Nat.succ n')) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.mul_add | [407, 1] | [414, 13] | induction n with
| zero => rfl
| succ n' ih =>
simp [add, mul, ih]
ac_rfl | l m n : ℕ
⊢ mul l (add m n) = add (mul l m) (mul l n) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.mul_add | [407, 1] | [414, 13] | rfl | case zero
l m : ℕ
⊢ mul l (add m Nat.zero) = add (mul l m) (mul l Nat.zero) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.mul_add | [407, 1] | [414, 13] | simp [add, mul, ih] | case succ
l m n' : ℕ
ih : mul l (add m n') = add (mul l m) (mul l n')
⊢ mul l (add m (Nat.succ n')) = add (mul l m) (mul l (Nat.succ n')) | case succ
l m n' : ℕ
ih : mul l (add m n') = add (mul l m) (mul l n')
⊢ add l (add (mul l m) (mul l n')) = add (mul l m) (add l (mul l n')) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.mul_add | [407, 1] | [414, 13] | ac_rfl | case succ
l m n' : ℕ
ih : mul l (add m n') = add (mul l m) (mul l n')
⊢ add l (add (mul l m) (mul l n')) = add (mul l m) (add l (mul l n')) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.cleanup_example | [424, 1] | [432, 12] | clear ha hab a | a b c : Prop
ha : a
hb : b
hab : a → b
hbc : b → c
⊢ c | b c : Prop
hb : b
hbc : b → c
⊢ c |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.cleanup_example | [424, 1] | [432, 12] | apply hbc | b c : Prop
hb : b
hbc : b → c
⊢ c | b c : Prop
hb : b
hbc : b → c
⊢ b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.cleanup_example | [424, 1] | [432, 12] | clear hbc c | b c : Prop
hb : b
hbc : b → c
⊢ b | b : Prop
hb : b
⊢ b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.cleanup_example | [424, 1] | [432, 12] | rename b => h | b : Prop
hb : b
⊢ b | b : Prop
h : b
⊢ b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.cleanup_example | [424, 1] | [432, 12] | exact h | b : Prop
h : b
⊢ b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.linarith_example | [235, 1] | [237, 14] | linarith | i : ℤ
hi : i > 5
⊢ 2 * i + 3 > 11 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Star_Star_Eq_Star | [244, 9] | [253, 29] | apply funext | α : Type
R : α → α → Prop
⊢ Star (Star R) = Star R | case h
α : Type
R : α → α → Prop
⊢ ∀ (x : α), Star (Star R) x = Star R x |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Star_Star_Eq_Star | [244, 9] | [253, 29] | intro a | case h
α : Type
R : α → α → Prop
⊢ ∀ (x : α), Star (Star R) x = Star R x | case h
α : Type
R : α → α → Prop
a : α
⊢ Star (Star R) a = Star R a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Star_Star_Eq_Star | [244, 9] | [253, 29] | apply funext | case h
α : Type
R : α → α → Prop
a : α
⊢ Star (Star R) a = Star R a | case h.h
α : Type
R : α → α → Prop
a : α
⊢ ∀ (x : α), Star (Star R) a x = Star R a x |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Star_Star_Eq_Star | [244, 9] | [253, 29] | intro b | case h.h
α : Type
R : α → α → Prop
a : α
⊢ ∀ (x : α), Star (Star R) a x = Star R a x | case h.h
α : Type
R : α → α → Prop
a b : α
⊢ Star (Star R) a b = Star R a b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Star_Star_Eq_Star | [244, 9] | [253, 29] | apply propext | case h.h
α : Type
R : α → α → Prop
a b : α
⊢ Star (Star R) a b = Star R a b | case h.h.a
α : Type
R : α → α → Prop
a b : α
⊢ Star (Star R) a b ↔ Star R a b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Star_Star_Eq_Star | [244, 9] | [253, 29] | apply Star_Star_Iff_Star | case h.h.a
α : Type
R : α → α → Prop
a b : α
⊢ Star (Star R) a b ↔ Star R a b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.cases_Eq_example | [278, 1] | [283, 10] | cases h | α : Type
l r : α
h : l = r
P : α → α → Prop
⊢ P l r | case refl
α : Type
l : α
P : α → α → Prop
⊢ P l l |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.cases_Eq_example | [278, 1] | [283, 10] | sorry | case refl
α : Type
l : α
P : α → α → Prop
⊢ P l l | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.cases_Classical_em_example | [288, 1] | [296, 22] | have hor : P a ∨ ¬ P a :=
Classical.em (P a) | α : Type
a : α
P Q : α → Prop
⊢ Q a | α : Type
a : α
P Q : α → Prop
hor : P a ∨ ¬P a
⊢ Q a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.cases_Classical_em_example | [288, 1] | [296, 22] | cases hor with
| inl hl => sorry
| inr hr => sorry | α : Type
a : α
P Q : α → Prop
hor : P a ∨ ¬P a
⊢ Q a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.cases_Classical_em_example | [288, 1] | [296, 22] | sorry | case inl
α : Type
a : α
P Q : α → Prop
hl : P a
⊢ Q a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.cases_Classical_em_example | [288, 1] | [296, 22] | sorry | case inr
α : Type
a : α
P Q : α → Prop
hr : ¬P a
⊢ Q a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Sorted_3_5 | [319, 1] | [324, 30] | apply Sorted.two_or_more | ⊢ Sorted [3, 5] | case hle
⊢ 3 ≤ 5
case hsorted
⊢ Sorted [5] |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Sorted_3_5 | [319, 1] | [324, 30] | { simp } | case hle
⊢ 3 ≤ 5
case hsorted
⊢ Sorted [5] | case hsorted
⊢ Sorted [5] |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Sorted_3_5 | [319, 1] | [324, 30] | { exact Sorted.single _ } | case hsorted
⊢ Sorted [5] | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Sorted_3_5 | [319, 1] | [324, 30] | simp | case hle
⊢ 3 ≤ 5 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Sorted_3_5 | [319, 1] | [324, 30] | exact Sorted.single _ | case hsorted
⊢ Sorted [5] | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Sorted_3_5_raw | [326, 1] | [328, 53] | simp | ⊢ 3 ≤ 5 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.sorted_7_9_9_11 | [330, 1] | [335, 30] | simp | ⊢ 7 ≤ 9 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.sorted_7_9_9_11 | [330, 1] | [335, 30] | simp | ⊢ 9 ≤ 9 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.sorted_7_9_9_11 | [330, 1] | [335, 30] | simp | ⊢ 9 ≤ 11 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Not_Sorted_17_13 | [337, 1] | [342, 51] | intro h | ⊢ ¬Sorted [17, 13] | h : Sorted [17, 13]
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Not_Sorted_17_13 | [337, 1] | [342, 51] | cases h with
| two_or_more _ _ hlet hsorted => simp at hlet | h : Sorted [17, 13]
⊢ False | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Not_Sorted_17_13 | [337, 1] | [342, 51] | simp at hlet | case two_or_more
hlet : 17 ≤ 13
hsorted : Sorted [13]
⊢ False | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Palindrome_reverse | [371, 1] | [380, 43] | induction hxs with
| nil => exact Palindrome.nil
| single x => exact Palindrome.single x
| sandwich x xs hxs ih =>
{ simp [reverse, reverse_append]
exact Palindrome.sandwich _ _ ih } | α : Type
xs : List α
hxs : Palindrome xs
⊢ Palindrome (reverse xs) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Palindrome_reverse | [371, 1] | [380, 43] | exact Palindrome.nil | case nil
α : Type
xs : List α
⊢ Palindrome (reverse []) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Palindrome_reverse | [371, 1] | [380, 43] | exact Palindrome.single x | case single
α : Type
xs : List α
x : α
⊢ Palindrome (reverse [x]) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Palindrome_reverse | [371, 1] | [380, 43] | simp [reverse, reverse_append] | case sandwich
α : Type
xs✝ : List α
x : α
xs : List α
hxs : Palindrome xs
ih : Palindrome (reverse xs)
⊢ Palindrome (reverse ([x] ++ xs ++ [x])) | case sandwich
α : Type
xs✝ : List α
x : α
xs : List α
hxs : Palindrome xs
ih : Palindrome (reverse xs)
⊢ Palindrome (x :: (reverse xs ++ [x])) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.Palindrome_reverse | [371, 1] | [380, 43] | exact Palindrome.sandwich _ _ ih | case sandwich
α : Type
xs✝ : List α
x : α
xs : List α
hxs : Palindrome xs
ih : Palindrome (reverse xs)
⊢ Palindrome (x :: (reverse xs ++ [x])) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_singleton | [394, 1] | [400, 12] | apply IsFull.node | α : Type
a : α
⊢ IsFull (BTree.node a BTree.empty BTree.empty) | case hl
α : Type
a : α
⊢ IsFull BTree.empty
case hr
α : Type
a : α
⊢ IsFull BTree.empty
case hiff
α : Type
a : α
⊢ BTree.empty = BTree.empty ↔ BTree.empty = BTree.empty |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_singleton | [394, 1] | [400, 12] | { exact IsFull.empty } | case hl
α : Type
a : α
⊢ IsFull BTree.empty
case hr
α : Type
a : α
⊢ IsFull BTree.empty
case hiff
α : Type
a : α
⊢ BTree.empty = BTree.empty ↔ BTree.empty = BTree.empty | case hr
α : Type
a : α
⊢ IsFull BTree.empty
case hiff
α : Type
a : α
⊢ BTree.empty = BTree.empty ↔ BTree.empty = BTree.empty |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_singleton | [394, 1] | [400, 12] | { exact IsFull.empty } | case hr
α : Type
a : α
⊢ IsFull BTree.empty
case hiff
α : Type
a : α
⊢ BTree.empty = BTree.empty ↔ BTree.empty = BTree.empty | case hiff
α : Type
a : α
⊢ BTree.empty = BTree.empty ↔ BTree.empty = BTree.empty |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_singleton | [394, 1] | [400, 12] | { rfl } | case hiff
α : Type
a : α
⊢ BTree.empty = BTree.empty ↔ BTree.empty = BTree.empty | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_singleton | [394, 1] | [400, 12] | exact IsFull.empty | case hl
α : Type
a : α
⊢ IsFull BTree.empty | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_singleton | [394, 1] | [400, 12] | exact IsFull.empty | case hr
α : Type
a : α
⊢ IsFull BTree.empty | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_singleton | [394, 1] | [400, 12] | rfl | case hiff
α : Type
a : α
⊢ BTree.empty = BTree.empty ↔ BTree.empty = BTree.empty | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_mirror | [402, 1] | [413, 44] | induction ht with
| empty => exact IsFull.empty
| node a l r hl hr hiff ih_l ih_r =>
{ rw [mirror]
apply IsFull.node
{ exact ih_r }
{ exact ih_l }
{ simp [mirror_Eq_empty_Iff, *] } } | α : Type
t : BTree α
ht : IsFull t
⊢ IsFull (mirror t) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_mirror | [402, 1] | [413, 44] | exact IsFull.empty | case empty
α : Type
t : BTree α
⊢ IsFull (mirror BTree.empty) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_mirror | [402, 1] | [413, 44] | rw [mirror] | case node
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ IsFull (mirror (BTree.node a l r)) | case node
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ IsFull (BTree.node a (mirror r) (mirror l)) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_mirror | [402, 1] | [413, 44] | apply IsFull.node | case node
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ IsFull (BTree.node a (mirror r) (mirror l)) | case node.hl
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ IsFull (mirror r)
case node.hr
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ IsFull (mirror l)
case node.hiff
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ mirror r = BTree.empty ↔ mirror l = BTree.empty |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_mirror | [402, 1] | [413, 44] | { exact ih_r } | case node.hl
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ IsFull (mirror r)
case node.hr
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ IsFull (mirror l)
case node.hiff
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ mirror r = BTree.empty ↔ mirror l = BTree.empty | case node.hr
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ IsFull (mirror l)
case node.hiff
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ mirror r = BTree.empty ↔ mirror l = BTree.empty |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_mirror | [402, 1] | [413, 44] | { exact ih_l } | case node.hr
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ IsFull (mirror l)
case node.hiff
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ mirror r = BTree.empty ↔ mirror l = BTree.empty | case node.hiff
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ mirror r = BTree.empty ↔ mirror l = BTree.empty |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_mirror | [402, 1] | [413, 44] | { simp [mirror_Eq_empty_Iff, *] } | case node.hiff
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ mirror r = BTree.empty ↔ mirror l = BTree.empty | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_mirror | [402, 1] | [413, 44] | exact ih_r | case node.hl
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ IsFull (mirror r) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_mirror | [402, 1] | [413, 44] | exact ih_l | case node.hr
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ IsFull (mirror l) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_mirror | [402, 1] | [413, 44] | simp [mirror_Eq_empty_Iff, *] | case node.hiff
α : Type
t : BTree α
a : α
l r : BTree α
hl : IsFull l
hr : IsFull r
hiff : l = BTree.empty ↔ r = BTree.empty
ih_l : IsFull (mirror l)
ih_r : IsFull (mirror r)
⊢ mirror r = BTree.empty ↔ mirror l = BTree.empty | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_mirror_struct_induct | [415, 1] | [430, 50] | induction t with
| empty =>
{ intro ht
exact ht }
| node a l r ih_l ih_r =>
{ intro ht
cases ht with
| node _ _ _ hl hr hiff =>
{ rw [mirror]
apply IsFull.node
{ exact ih_r hr }
{ apply ih_l hl }
{ simp [mirror_Eq_empty_Iff, *] } } } | α : Type
t : BTree α
⊢ IsFull t → IsFull (mirror t) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_mirror_struct_induct | [415, 1] | [430, 50] | intro ht | case empty
α : Type
⊢ IsFull BTree.empty → IsFull (mirror BTree.empty) | case empty
α : Type
ht : IsFull BTree.empty
⊢ IsFull (mirror BTree.empty) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_mirror_struct_induct | [415, 1] | [430, 50] | exact ht | case empty
α : Type
ht : IsFull BTree.empty
⊢ IsFull (mirror BTree.empty) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_mirror_struct_induct | [415, 1] | [430, 50] | intro ht | case node
α : Type
a : α
l r : BTree α
ih_l : IsFull l → IsFull (mirror l)
ih_r : IsFull r → IsFull (mirror r)
⊢ IsFull (BTree.node a l r) → IsFull (mirror (BTree.node a l r)) | case node
α : Type
a : α
l r : BTree α
ih_l : IsFull l → IsFull (mirror l)
ih_r : IsFull r → IsFull (mirror r)
ht : IsFull (BTree.node a l r)
⊢ IsFull (mirror (BTree.node a l r)) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe06_InductivePredicates_Demo.lean | LoVe.IsFull_mirror_struct_induct | [415, 1] | [430, 50] | cases ht with
| node _ _ _ hl hr hiff =>
{ rw [mirror]
apply IsFull.node
{ exact ih_r hr }
{ apply ih_l hl }
{ simp [mirror_Eq_empty_Iff, *] } } | case node
α : Type
a : α
l r : BTree α
ih_l : IsFull l → IsFull (mirror l)
ih_r : IsFull r → IsFull (mirror r)
ht : IsFull (BTree.node a l r)
⊢ IsFull (mirror (BTree.node a l r)) | no goals |
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