url
stringclasses 147
values | commit
stringclasses 147
values | file_path
stringlengths 7
101
| full_name
stringlengths 1
94
| start
stringlengths 6
10
| end
stringlengths 6
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| tactic
stringlengths 1
11.2k
| state_before
stringlengths 3
2.09M
| state_after
stringlengths 6
2.09M
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|---|---|---|---|---|---|---|---|---|
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.add_comm_zero_left_by_exact | [40, 1] | [42, 24] | exact add_comm 0 n | n : ℕ
⊢ add 0 n = add n 0 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.nat_exists_double_iden | [116, 1] | [120, 13] | rfl | ⊢ double 0 = 0 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.nat_exists_double_iden_no_show | [122, 1] | [124, 26] | rfl | ⊢ double 0 = 0 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.Forall.one_point | [143, 1] | [157, 19] | apply hall t | α : Type
t : α
P : α → Prop
hall : ∀ (x : α), x = t → P x
⊢ P t | α : Type
t : α
P : α → Prop
hall : ∀ (x : α), x = t → P x
⊢ t = t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.Forall.one_point | [143, 1] | [157, 19] | rfl | α : Type
t : α
P : α → Prop
hall : ∀ (x : α), x = t → P x
⊢ t = t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.Forall.one_point | [143, 1] | [157, 19] | rw [heq] | α : Type
t : α
P : α → Prop
hp : P t
x : α
heq : x = t
⊢ P x | α : Type
t : α
P : α → Prop
hp : P t
x : α
heq : x = t
⊢ P t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.Forall.one_point | [143, 1] | [157, 19] | exact hp | α : Type
t : α
P : α → Prop
hp : P t
x : α
heq : x = t
⊢ P t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.Exists.one_point | [165, 1] | [187, 30] | rw [←hxt] | α : Type
t : α
P : α → Prop
hex : ∃ x, x = t ∧ P x
x : α
hand : x = t ∧ P x
hxt : x = t
hpx : P x
⊢ P t | α : Type
t : α
P : α → Prop
hex : ∃ x, x = t ∧ P x
x : α
hand : x = t ∧ P x
hxt : x = t
hpx : P x
⊢ P x |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.Exists.one_point | [165, 1] | [187, 30] | exact hpx | α : Type
t : α
P : α → Prop
hex : ∃ x, x = t ∧ P x
x : α
hand : x = t ∧ P x
hxt : x = t
hpx : P x
⊢ P x | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.Exists.one_point | [165, 1] | [187, 30] | rfl | α : Type
t : α
P : α → Prop
hp : P t
⊢ t = t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.two_mul_example | [207, 1] | [213, 14] | rw [Nat.two_mul] | m n : ℕ
⊢ 2 * m + n = m + m + n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.two_mul_example | [207, 1] | [213, 14] | ac_rfl | m n : ℕ
⊢ m + m + n = m + n + m | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.two_mul_example_have | [218, 1] | [225, 24] | rw [Nat.two_mul] | m n : ℕ
⊢ 2 * m + n = m + m + n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.two_mul_example_have | [218, 1] | [225, 24] | ac_rfl | m n : ℕ
hmul : 2 * m + n = m + m + n
⊢ m + m + n = m + n + m | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.prop_comp_tactical | [234, 1] | [244, 13] | intro ha | a b c : Prop
hab : a → b
hbc : b → c
⊢ a → c | a b c : Prop
hab : a → b
hbc : b → c
ha : a
⊢ c |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.prop_comp_tactical | [234, 1] | [244, 13] | have hb : b :=
hab ha | a b c : Prop
hab : a → b
hbc : b → c
ha : a
⊢ c | a b c : Prop
hab : a → b
hbc : b → c
ha : a
hb : b
⊢ c |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.prop_comp_tactical | [234, 1] | [244, 13] | let c' := c | a b c : Prop
hab : a → b
hbc : b → c
ha : a
hb : b
⊢ c | a b c : Prop
hab : a → b
hbc : b → c
ha : a
hb : b
c' : Prop := c
⊢ c |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.prop_comp_tactical | [234, 1] | [244, 13] | have hc : c' :=
hbc hb | a b c : Prop
hab : a → b
hbc : b → c
ha : a
hb : b
c' : Prop := c
⊢ c | a b c : Prop
hab : a → b
hbc : b → c
ha : a
hb : b
c' : Prop := c
hc : c'
⊢ c |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.prop_comp_tactical | [234, 1] | [244, 13] | exact hc | a b c : Prop
hab : a → b
hbc : b → c
ha : a
hb : b
c' : Prop := c
hc : c'
⊢ c | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.And_swap_tactical | [386, 1] | [394, 14] | intro hab | a b : Prop
⊢ a ∧ b → b ∧ a | a b : Prop
hab : a ∧ b
⊢ b ∧ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.And_swap_tactical | [386, 1] | [394, 14] | apply And.intro | a b : Prop
hab : a ∧ b
⊢ b ∧ a | case left
a b : Prop
hab : a ∧ b
⊢ b
case right
a b : Prop
hab : a ∧ b
⊢ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.And_swap_tactical | [386, 1] | [394, 14] | apply And.right | case left
a b : Prop
hab : a ∧ b
⊢ b
case right
a b : Prop
hab : a ∧ b
⊢ a | case left.self
a b : Prop
hab : a ∧ b
⊢ ?left.a ∧ b
case left.a
a b : Prop
hab : a ∧ b
⊢ Prop
case right
a b : Prop
hab : a ∧ b
⊢ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.And_swap_tactical | [386, 1] | [394, 14] | exact hab | case left.self
a b : Prop
hab : a ∧ b
⊢ ?left.a ∧ b
case left.a
a b : Prop
hab : a ∧ b
⊢ Prop
case right
a b : Prop
hab : a ∧ b
⊢ a | case right
a b : Prop
hab : a ∧ b
⊢ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.And_swap_tactical | [386, 1] | [394, 14] | apply And.left | case right
a b : Prop
hab : a ∧ b
⊢ a | case right.self
a b : Prop
hab : a ∧ b
⊢ a ∧ ?right.b
case right.b
a b : Prop
hab : a ∧ b
⊢ Prop |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.ForwardProofs.And_swap_tactical | [386, 1] | [394, 14] | exact hab | case right.self
a b : Prop
hab : a ∧ b
⊢ a ∧ ?right.b
case right.b
a b : Prop
hab : a ∧ b
⊢ Prop | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.reverse_append | [448, 1] | [452, 56] | simp [reverse] | α : Type
ys : List α
⊢ reverse ([] ++ ys) = reverse ys ++ reverse [] | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.reverse_append | [448, 1] | [452, 56] | simp [reverse, reverse_append xs] | α : Type
x : α
xs ys : List α
⊢ reverse (x :: xs ++ ys) = reverse ys ++ reverse (x :: xs) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.reverse_append_tactical | [454, 1] | [459, 42] | induction xs with
| nil => simp [reverse]
| cons x xs' ih => simp [reverse, ih] | α : Type
xs ys : List α
⊢ reverse (xs ++ ys) = reverse ys ++ reverse xs | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.reverse_append_tactical | [454, 1] | [459, 42] | simp [reverse] | case nil
α : Type
ys : List α
⊢ reverse ([] ++ ys) = reverse ys ++ reverse [] | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.reverse_append_tactical | [454, 1] | [459, 42] | simp [reverse, ih] | case cons
α : Type
ys : List α
x : α
xs' : List α
ih : reverse (xs' ++ ys) = reverse ys ++ reverse xs'
⊢ reverse (x :: xs' ++ ys) = reverse ys ++ reverse (x :: xs') | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.reverse_reverse | [461, 1] | [465, 58] | rfl | α : Type
⊢ reverse (reverse []) = [] | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe04_ForwardProofs_Demo.lean | LoVe.reverse_reverse | [461, 1] | [465, 58] | simp [reverse, reverse_append, reverse_reverse xs] | α : Type
x : α
xs : List α
⊢ reverse (reverse (x :: xs)) = x :: xs | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Homework/Homework3.lean | LoVe.about_Impl | [23, 1] | [33, 17] | intros a b hor ha | ⊢ ∀ (a b : Prop), ¬a ∨ b → a → b | a b : Prop
hor : ¬a ∨ b
ha : a
⊢ b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Homework/Homework3.lean | LoVe.about_Impl | [23, 1] | [33, 17] | apply Or.elim hor | a b : Prop
hor : ¬a ∨ b
ha : a
⊢ b | case left
a b : Prop
hor : ¬a ∨ b
ha : a
⊢ ¬a → b
case right
a b : Prop
hor : ¬a ∨ b
ha : a
⊢ b → b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Homework/Homework3.lean | LoVe.about_Impl | [23, 1] | [33, 17] | { intro hna
apply False.elim
apply hna
exact ha } | case left
a b : Prop
hor : ¬a ∨ b
ha : a
⊢ ¬a → b
case right
a b : Prop
hor : ¬a ∨ b
ha : a
⊢ b → b | case right
a b : Prop
hor : ¬a ∨ b
ha : a
⊢ b → b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Homework/Homework3.lean | LoVe.about_Impl | [23, 1] | [33, 17] | { intro hb
exact hb } | case right
a b : Prop
hor : ¬a ∨ b
ha : a
⊢ b → b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Homework/Homework3.lean | LoVe.about_Impl | [23, 1] | [33, 17] | intro hna | case left
a b : Prop
hor : ¬a ∨ b
ha : a
⊢ ¬a → b | case left
a b : Prop
hor : ¬a ∨ b
ha : a
hna : ¬a
⊢ b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Homework/Homework3.lean | LoVe.about_Impl | [23, 1] | [33, 17] | apply False.elim | case left
a b : Prop
hor : ¬a ∨ b
ha : a
hna : ¬a
⊢ b | case left.h
a b : Prop
hor : ¬a ∨ b
ha : a
hna : ¬a
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Homework/Homework3.lean | LoVe.about_Impl | [23, 1] | [33, 17] | apply hna | case left.h
a b : Prop
hor : ¬a ∨ b
ha : a
hna : ¬a
⊢ False | case left.h
a b : Prop
hor : ¬a ∨ b
ha : a
hna : ¬a
⊢ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Homework/Homework3.lean | LoVe.about_Impl | [23, 1] | [33, 17] | exact ha | case left.h
a b : Prop
hor : ¬a ∨ b
ha : a
hna : ¬a
⊢ a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Homework/Homework3.lean | LoVe.about_Impl | [23, 1] | [33, 17] | intro hb | case right
a b : Prop
hor : ¬a ∨ b
ha : a
⊢ b → b | case right
a b : Prop
hor : ¬a ∨ b
ha : a
hb : b
⊢ b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Homework/Homework3.lean | LoVe.about_Impl | [23, 1] | [33, 17] | exact hb | case right
a b : Prop
hor : ¬a ∨ b
ha : a
hb : b
⊢ b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assign_iff | [76, 9] | [85, 29] | apply Iff.intro | x : String
a : State → ℕ
s t : State
⊢ (Stmt.assign x a, s) ⟹ t ↔ t = State.update x (a s) s | case mp
x : String
a : State → ℕ
s t : State
⊢ (Stmt.assign x a, s) ⟹ t → t = State.update x (a s) s
case mpr
x : String
a : State → ℕ
s t : State
⊢ t = State.update x (a s) s → (Stmt.assign x a, s) ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assign_iff | [76, 9] | [85, 29] | { intro hasn
cases hasn
rfl } | case mp
x : String
a : State → ℕ
s t : State
⊢ (Stmt.assign x a, s) ⟹ t → t = State.update x (a s) s
case mpr
x : String
a : State → ℕ
s t : State
⊢ t = State.update x (a s) s → (Stmt.assign x a, s) ⟹ t | case mpr
x : String
a : State → ℕ
s t : State
⊢ t = State.update x (a s) s → (Stmt.assign x a, s) ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assign_iff | [76, 9] | [85, 29] | { intro heq
rw [heq]
apply BigStep.assign } | case mpr
x : String
a : State → ℕ
s t : State
⊢ t = State.update x (a s) s → (Stmt.assign x a, s) ⟹ t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assign_iff | [76, 9] | [85, 29] | intro hasn | case mp
x : String
a : State → ℕ
s t : State
⊢ (Stmt.assign x a, s) ⟹ t → t = State.update x (a s) s | case mp
x : String
a : State → ℕ
s t : State
hasn : (Stmt.assign x a, s) ⟹ t
⊢ t = State.update x (a s) s |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assign_iff | [76, 9] | [85, 29] | cases hasn | case mp
x : String
a : State → ℕ
s t : State
hasn : (Stmt.assign x a, s) ⟹ t
⊢ t = State.update x (a s) s | case mp.assign
x : String
a : State → ℕ
s : State
⊢ State.update x (a s) s = State.update x (a s) s |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assign_iff | [76, 9] | [85, 29] | rfl | case mp.assign
x : String
a : State → ℕ
s : State
⊢ State.update x (a s) s = State.update x (a s) s | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assign_iff | [76, 9] | [85, 29] | intro heq | case mpr
x : String
a : State → ℕ
s t : State
⊢ t = State.update x (a s) s → (Stmt.assign x a, s) ⟹ t | case mpr
x : String
a : State → ℕ
s t : State
heq : t = State.update x (a s) s
⊢ (Stmt.assign x a, s) ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assign_iff | [76, 9] | [85, 29] | rw [heq] | case mpr
x : String
a : State → ℕ
s t : State
heq : t = State.update x (a s) s
⊢ (Stmt.assign x a, s) ⟹ t | case mpr
x : String
a : State → ℕ
s t : State
heq : t = State.update x (a s) s
⊢ (Stmt.assign x a, s) ⟹ State.update x (a s) s |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assign_iff | [76, 9] | [85, 29] | apply BigStep.assign | case mpr
x : String
a : State → ℕ
s t : State
heq : t = State.update x (a s) s
⊢ (Stmt.assign x a, s) ⟹ State.update x (a s) s | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assert | [87, 9] | [99, 19] | apply Iff.intro | B : State → Prop
s t : State
⊢ (Stmt.assert B, s) ⟹ t ↔ t = s ∧ B s | case mp
B : State → Prop
s t : State
⊢ (Stmt.assert B, s) ⟹ t → t = s ∧ B s
case mpr
B : State → Prop
s t : State
⊢ t = s ∧ B s → (Stmt.assert B, s) ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assert | [87, 9] | [99, 19] | { intro hast
cases hast
simp [*] } | case mp
B : State → Prop
s t : State
⊢ (Stmt.assert B, s) ⟹ t → t = s ∧ B s
case mpr
B : State → Prop
s t : State
⊢ t = s ∧ B s → (Stmt.assert B, s) ⟹ t | case mpr
B : State → Prop
s t : State
⊢ t = s ∧ B s → (Stmt.assert B, s) ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assert | [87, 9] | [99, 19] | { intro hand
cases hand with
| intro hts hB =>
rw [hts]
apply BigStep.assert
exact hB } | case mpr
B : State → Prop
s t : State
⊢ t = s ∧ B s → (Stmt.assert B, s) ⟹ t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assert | [87, 9] | [99, 19] | intro hast | case mp
B : State → Prop
s t : State
⊢ (Stmt.assert B, s) ⟹ t → t = s ∧ B s | case mp
B : State → Prop
s t : State
hast : (Stmt.assert B, s) ⟹ t
⊢ t = s ∧ B s |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assert | [87, 9] | [99, 19] | cases hast | case mp
B : State → Prop
s t : State
hast : (Stmt.assert B, s) ⟹ t
⊢ t = s ∧ B s | case mp.assert
B : State → Prop
s : State
hB✝ : B s
⊢ s = s ∧ B s |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assert | [87, 9] | [99, 19] | simp [*] | case mp.assert
B : State → Prop
s : State
hB✝ : B s
⊢ s = s ∧ B s | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assert | [87, 9] | [99, 19] | intro hand | case mpr
B : State → Prop
s t : State
⊢ t = s ∧ B s → (Stmt.assert B, s) ⟹ t | case mpr
B : State → Prop
s t : State
hand : t = s ∧ B s
⊢ (Stmt.assert B, s) ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assert | [87, 9] | [99, 19] | cases hand with
| intro hts hB =>
rw [hts]
apply BigStep.assert
exact hB | case mpr
B : State → Prop
s t : State
hand : t = s ∧ B s
⊢ (Stmt.assert B, s) ⟹ t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assert | [87, 9] | [99, 19] | rw [hts] | case mpr.intro
B : State → Prop
s t : State
hts : t = s
hB : B s
⊢ (Stmt.assert B, s) ⟹ t | case mpr.intro
B : State → Prop
s t : State
hts : t = s
hB : B s
⊢ (Stmt.assert B, s) ⟹ s |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assert | [87, 9] | [99, 19] | apply BigStep.assert | case mpr.intro
B : State → Prop
s t : State
hts : t = s
hB : B s
⊢ (Stmt.assert B, s) ⟹ s | case mpr.intro.hB
B : State → Prop
s t : State
hts : t = s
hB : B s
⊢ B s |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_assert | [87, 9] | [99, 19] | exact hB | case mpr.intro.hB
B : State → Prop
s t : State
hts : t = s
hB : B s
⊢ B s | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_seq_iff | [101, 9] | [116, 25] | apply Iff.intro | S₁ S₂ : Stmt
s t : State
⊢ (S₁; S₂, s) ⟹ t ↔ ∃ u, (S₁, s) ⟹ u ∧ (S₂, u) ⟹ t | case mp
S₁ S₂ : Stmt
s t : State
⊢ (S₁; S₂, s) ⟹ t → ∃ u, (S₁, s) ⟹ u ∧ (S₂, u) ⟹ t
case mpr
S₁ S₂ : Stmt
s t : State
⊢ (∃ u, (S₁, s) ⟹ u ∧ (S₂, u) ⟹ t) → (S₁; S₂, s) ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_seq_iff | [101, 9] | [116, 25] | { intro hseq
cases hseq
apply Exists.intro
apply And.intro <;>
assumption } | case mp
S₁ S₂ : Stmt
s t : State
⊢ (S₁; S₂, s) ⟹ t → ∃ u, (S₁, s) ⟹ u ∧ (S₂, u) ⟹ t
case mpr
S₁ S₂ : Stmt
s t : State
⊢ (∃ u, (S₁, s) ⟹ u ∧ (S₂, u) ⟹ t) → (S₁; S₂, s) ⟹ t | case mpr
S₁ S₂ : Stmt
s t : State
⊢ (∃ u, (S₁, s) ⟹ u ∧ (S₂, u) ⟹ t) → (S₁; S₂, s) ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_seq_iff | [101, 9] | [116, 25] | { intro hseq
cases hseq with
| intro u hand =>
cases hand with
| intro hS₁ hS₂ =>
apply BigStep.seq <;>
assumption } | case mpr
S₁ S₂ : Stmt
s t : State
⊢ (∃ u, (S₁, s) ⟹ u ∧ (S₂, u) ⟹ t) → (S₁; S₂, s) ⟹ t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_seq_iff | [101, 9] | [116, 25] | intro hseq | case mp
S₁ S₂ : Stmt
s t : State
⊢ (S₁; S₂, s) ⟹ t → ∃ u, (S₁, s) ⟹ u ∧ (S₂, u) ⟹ t | case mp
S₁ S₂ : Stmt
s t : State
hseq : (S₁; S₂, s) ⟹ t
⊢ ∃ u, (S₁, s) ⟹ u ∧ (S₂, u) ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_seq_iff | [101, 9] | [116, 25] | cases hseq | case mp
S₁ S₂ : Stmt
s t : State
hseq : (S₁; S₂, s) ⟹ t
⊢ ∃ u, (S₁, s) ⟹ u ∧ (S₂, u) ⟹ t | case mp.seq
S₁ S₂ : Stmt
s t t✝ : State
hS✝ : (S₁, s) ⟹ t✝
hT✝ : (S₂, t✝) ⟹ t
⊢ ∃ u, (S₁, s) ⟹ u ∧ (S₂, u) ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_seq_iff | [101, 9] | [116, 25] | apply Exists.intro | case mp.seq
S₁ S₂ : Stmt
s t t✝ : State
hS✝ : (S₁, s) ⟹ t✝
hT✝ : (S₂, t✝) ⟹ t
⊢ ∃ u, (S₁, s) ⟹ u ∧ (S₂, u) ⟹ t | case mp.seq.h
S₁ S₂ : Stmt
s t t✝ : State
hS✝ : (S₁, s) ⟹ t✝
hT✝ : (S₂, t✝) ⟹ t
⊢ (S₁, s) ⟹ ?mp.seq.w ∧ (S₂, ?mp.seq.w) ⟹ t
case mp.seq.w
S₁ S₂ : Stmt
s t t✝ : State
hS✝ : (S₁, s) ⟹ t✝
hT✝ : (S₂, t✝) ⟹ t
⊢ State |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_seq_iff | [101, 9] | [116, 25] | apply And.intro <;>
assumption | case mp.seq.h
S₁ S₂ : Stmt
s t t✝ : State
hS✝ : (S₁, s) ⟹ t✝
hT✝ : (S₂, t✝) ⟹ t
⊢ (S₁, s) ⟹ ?mp.seq.w ∧ (S₂, ?mp.seq.w) ⟹ t
case mp.seq.w
S₁ S₂ : Stmt
s t t✝ : State
hS✝ : (S₁, s) ⟹ t✝
hT✝ : (S₂, t✝) ⟹ t
⊢ State | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_seq_iff | [101, 9] | [116, 25] | intro hseq | case mpr
S₁ S₂ : Stmt
s t : State
⊢ (∃ u, (S₁, s) ⟹ u ∧ (S₂, u) ⟹ t) → (S₁; S₂, s) ⟹ t | case mpr
S₁ S₂ : Stmt
s t : State
hseq : ∃ u, (S₁, s) ⟹ u ∧ (S₂, u) ⟹ t
⊢ (S₁; S₂, s) ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_seq_iff | [101, 9] | [116, 25] | cases hseq with
| intro u hand =>
cases hand with
| intro hS₁ hS₂ =>
apply BigStep.seq <;>
assumption | case mpr
S₁ S₂ : Stmt
s t : State
hseq : ∃ u, (S₁, s) ⟹ u ∧ (S₂, u) ⟹ t
⊢ (S₁; S₂, s) ⟹ t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_seq_iff | [101, 9] | [116, 25] | cases hand with
| intro hS₁ hS₂ =>
apply BigStep.seq <;>
assumption | case mpr.intro
S₁ S₂ : Stmt
s t u : State
hand : (S₁, s) ⟹ u ∧ (S₂, u) ⟹ t
⊢ (S₁; S₂, s) ⟹ t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_seq_iff | [101, 9] | [116, 25] | apply BigStep.seq <;>
assumption | case mpr.intro.intro
S₁ S₂ : Stmt
s t u : State
hS₁ : (S₁, s) ⟹ u
hS₂ : (S₂, u) ⟹ t
⊢ (S₁; S₂, s) ⟹ t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_loop | [118, 1] | [143, 27] | apply Iff.intro | S : Stmt
s u : State
⊢ (Stmt.loop S, s) ⟹ u ↔ s = u ∨ ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u | case mp
S : Stmt
s u : State
⊢ (Stmt.loop S, s) ⟹ u → s = u ∨ ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u
case mpr
S : Stmt
s u : State
⊢ (s = u ∨ ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u) → (Stmt.loop S, s) ⟹ u |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_loop | [118, 1] | [143, 27] | { intro hloop
cases hloop with
| loop_base S s =>
apply Or.inl
rfl
| loop_step S s t u hS hl =>
apply Or.inr
apply Exists.intro t
aesop } | case mp
S : Stmt
s u : State
⊢ (Stmt.loop S, s) ⟹ u → s = u ∨ ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u
case mpr
S : Stmt
s u : State
⊢ (s = u ∨ ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u) → (Stmt.loop S, s) ⟹ u | case mpr
S : Stmt
s u : State
⊢ (s = u ∨ ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u) → (Stmt.loop S, s) ⟹ u |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_loop | [118, 1] | [143, 27] | { intro hor
cases hor with
| inl hsu =>
rw [hsu]
apply BigStep.loop_base
| inr hex =>
cases hex with
| intro t hand =>
cases hand with
| intro hS hl =>
apply BigStep.loop_step <;>
assumption } | case mpr
S : Stmt
s u : State
⊢ (s = u ∨ ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u) → (Stmt.loop S, s) ⟹ u | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_loop | [118, 1] | [143, 27] | intro hloop | case mp
S : Stmt
s u : State
⊢ (Stmt.loop S, s) ⟹ u → s = u ∨ ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u | case mp
S : Stmt
s u : State
hloop : (Stmt.loop S, s) ⟹ u
⊢ s = u ∨ ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_loop | [118, 1] | [143, 27] | cases hloop with
| loop_base S s =>
apply Or.inl
rfl
| loop_step S s t u hS hl =>
apply Or.inr
apply Exists.intro t
aesop | case mp
S : Stmt
s u : State
hloop : (Stmt.loop S, s) ⟹ u
⊢ s = u ∨ ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_loop | [118, 1] | [143, 27] | apply Or.inl | case mp.loop_base
S : Stmt
s : State
⊢ s = s ∨ ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ s | case mp.loop_base.h
S : Stmt
s : State
⊢ s = s |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_loop | [118, 1] | [143, 27] | rfl | case mp.loop_base.h
S : Stmt
s : State
⊢ s = s | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_loop | [118, 1] | [143, 27] | apply Or.inr | case mp.loop_step
S : Stmt
s u t : State
hS : (S, s) ⟹ t
hl : (Stmt.loop S, t) ⟹ u
⊢ s = u ∨ ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u | case mp.loop_step.h
S : Stmt
s u t : State
hS : (S, s) ⟹ t
hl : (Stmt.loop S, t) ⟹ u
⊢ ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_loop | [118, 1] | [143, 27] | apply Exists.intro t | case mp.loop_step.h
S : Stmt
s u t : State
hS : (S, s) ⟹ t
hl : (Stmt.loop S, t) ⟹ u
⊢ ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u | case mp.loop_step.h
S : Stmt
s u t : State
hS : (S, s) ⟹ t
hl : (Stmt.loop S, t) ⟹ u
⊢ (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_loop | [118, 1] | [143, 27] | aesop | case mp.loop_step.h
S : Stmt
s u t : State
hS : (S, s) ⟹ t
hl : (Stmt.loop S, t) ⟹ u
⊢ (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_loop | [118, 1] | [143, 27] | intro hor | case mpr
S : Stmt
s u : State
⊢ (s = u ∨ ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u) → (Stmt.loop S, s) ⟹ u | case mpr
S : Stmt
s u : State
hor : s = u ∨ ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u
⊢ (Stmt.loop S, s) ⟹ u |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_loop | [118, 1] | [143, 27] | cases hor with
| inl hsu =>
rw [hsu]
apply BigStep.loop_base
| inr hex =>
cases hex with
| intro t hand =>
cases hand with
| intro hS hl =>
apply BigStep.loop_step <;>
assumption | case mpr
S : Stmt
s u : State
hor : s = u ∨ ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u
⊢ (Stmt.loop S, s) ⟹ u | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_loop | [118, 1] | [143, 27] | rw [hsu] | case mpr.inl
S : Stmt
s u : State
hsu : s = u
⊢ (Stmt.loop S, s) ⟹ u | case mpr.inl
S : Stmt
s u : State
hsu : s = u
⊢ (Stmt.loop S, u) ⟹ u |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_loop | [118, 1] | [143, 27] | apply BigStep.loop_base | case mpr.inl
S : Stmt
s u : State
hsu : s = u
⊢ (Stmt.loop S, u) ⟹ u | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_loop | [118, 1] | [143, 27] | cases hex with
| intro t hand =>
cases hand with
| intro hS hl =>
apply BigStep.loop_step <;>
assumption | case mpr.inr
S : Stmt
s u : State
hex : ∃ t, (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u
⊢ (Stmt.loop S, s) ⟹ u | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_loop | [118, 1] | [143, 27] | cases hand with
| intro hS hl =>
apply BigStep.loop_step <;>
assumption | case mpr.inr.intro
S : Stmt
s u t : State
hand : (S, s) ⟹ t ∧ (Stmt.loop S, t) ⟹ u
⊢ (Stmt.loop S, s) ⟹ u | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_loop | [118, 1] | [143, 27] | apply BigStep.loop_step <;>
assumption | case mpr.inr.intro.intro
S : Stmt
s u t : State
hS : (S, s) ⟹ t
hl : (Stmt.loop S, t) ⟹ u
⊢ (Stmt.loop S, s) ⟹ u | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_choice | [147, 9] | [164, 23] | apply Iff.intro | Ss : List Stmt
s t : State
⊢ (Stmt.choice Ss, s) ⟹ t ↔ ∃ i hless, (Ss[i], s) ⟹ t | case mp
Ss : List Stmt
s t : State
⊢ (Stmt.choice Ss, s) ⟹ t → ∃ i hless, (Ss[i], s) ⟹ t
case mpr
Ss : List Stmt
s t : State
⊢ (∃ i hless, (Ss[i], s) ⟹ t) → (Stmt.choice Ss, s) ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_choice | [147, 9] | [164, 23] | { intro hchoice
cases hchoice with
| choice _ _ _ i hless hbody =>
apply Exists.intro i
apply Exists.intro hless
assumption } | case mp
Ss : List Stmt
s t : State
⊢ (Stmt.choice Ss, s) ⟹ t → ∃ i hless, (Ss[i], s) ⟹ t
case mpr
Ss : List Stmt
s t : State
⊢ (∃ i hless, (Ss[i], s) ⟹ t) → (Stmt.choice Ss, s) ⟹ t | case mpr
Ss : List Stmt
s t : State
⊢ (∃ i hless, (Ss[i], s) ⟹ t) → (Stmt.choice Ss, s) ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_choice | [147, 9] | [164, 23] | { intro hex
cases hex with
| intro i hex =>
cases hex with
| intro hless hstep =>
apply BigStep.choice <;>
assumption } | case mpr
Ss : List Stmt
s t : State
⊢ (∃ i hless, (Ss[i], s) ⟹ t) → (Stmt.choice Ss, s) ⟹ t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_choice | [147, 9] | [164, 23] | intro hchoice | case mp
Ss : List Stmt
s t : State
⊢ (Stmt.choice Ss, s) ⟹ t → ∃ i hless, (Ss[i], s) ⟹ t | case mp
Ss : List Stmt
s t : State
hchoice : (Stmt.choice Ss, s) ⟹ t
⊢ ∃ i hless, (Ss[i], s) ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_choice | [147, 9] | [164, 23] | cases hchoice with
| choice _ _ _ i hless hbody =>
apply Exists.intro i
apply Exists.intro hless
assumption | case mp
Ss : List Stmt
s t : State
hchoice : (Stmt.choice Ss, s) ⟹ t
⊢ ∃ i hless, (Ss[i], s) ⟹ t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_choice | [147, 9] | [164, 23] | apply Exists.intro i | case mp.choice
Ss : List Stmt
s t : State
i : ℕ
hless : i < List.length Ss
hbody : (Ss[i], s) ⟹ t
⊢ ∃ i hless, (Ss[i], s) ⟹ t | case mp.choice
Ss : List Stmt
s t : State
i : ℕ
hless : i < List.length Ss
hbody : (Ss[i], s) ⟹ t
⊢ ∃ hless, (Ss[i], s) ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_choice | [147, 9] | [164, 23] | apply Exists.intro hless | case mp.choice
Ss : List Stmt
s t : State
i : ℕ
hless : i < List.length Ss
hbody : (Ss[i], s) ⟹ t
⊢ ∃ hless, (Ss[i], s) ⟹ t | case mp.choice
Ss : List Stmt
s t : State
i : ℕ
hless : i < List.length Ss
hbody : (Ss[i], s) ⟹ t
⊢ (Ss[i], s) ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_choice | [147, 9] | [164, 23] | assumption | case mp.choice
Ss : List Stmt
s t : State
i : ℕ
hless : i < List.length Ss
hbody : (Ss[i], s) ⟹ t
⊢ (Ss[i], s) ⟹ t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_choice | [147, 9] | [164, 23] | intro hex | case mpr
Ss : List Stmt
s t : State
⊢ (∃ i hless, (Ss[i], s) ⟹ t) → (Stmt.choice Ss, s) ⟹ t | case mpr
Ss : List Stmt
s t : State
hex : ∃ i hless, (Ss[i], s) ⟹ t
⊢ (Stmt.choice Ss, s) ⟹ t |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab6Solution.lean | LoVe.GCL.BigStep_choice | [147, 9] | [164, 23] | cases hex with
| intro i hex =>
cases hex with
| intro hless hstep =>
apply BigStep.choice <;>
assumption | case mpr
Ss : List Stmt
s t : State
hex : ∃ i hless, (Ss[i], s) ⟹ t
⊢ (Stmt.choice Ss, s) ⟹ t | no goals |
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