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 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/fpvandoorn/LeanCourse23.git | 7b0a3cf61b802764dc7baee9d9825e9c62cf9c5d | LeanCourse/MIL/C06_Structures/S03_Building_the_Gaussian_Integers.lean | gaussInt.not_norm_mul_left_lt_norm | [247, 1] | [254, 51] | rw [coe_natAbs_norm] | case h
x y : gaussInt
hy : y ≠ 0
⊢ ↑1 ≤ ↑(Int.natAbs (norm y)) | case h
x y : gaussInt
hy : y ≠ 0
⊢ ↑1 ≤ norm y | Please generate a tactic in lean4 to solve the state.
STATE:
case h
x y : gaussInt
hy : y ≠ 0
⊢ ↑1 ≤ ↑(Int.natAbs (norm y))
TACTIC:
|
https://github.com/fpvandoorn/LeanCourse23.git | 7b0a3cf61b802764dc7baee9d9825e9c62cf9c5d | LeanCourse/MIL/C06_Structures/S03_Building_the_Gaussian_Integers.lean | gaussInt.not_norm_mul_left_lt_norm | [247, 1] | [254, 51] | exact Int.add_one_le_of_lt ((norm_pos _).mpr hy) | case h
x y : gaussInt
hy : y ≠ 0
⊢ ↑1 ≤ norm y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
x y : gaussInt
hy : y ≠ 0
⊢ ↑1 ≤ norm y
TACTIC:
|
https://github.com/fpvandoorn/LeanCourse23.git | 7b0a3cf61b802764dc7baee9d9825e9c62cf9c5d | LeanCourse/Lectures/Lecture8Before.lean | Point.add_commutative | [135, 1] | [135, 93] | simp [add, add_comm] | n : ℕ
a b : Point
⊢ add a b = add b a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
a b : Point
⊢ add a b = add b a
TACTIC:
|
https://github.com/fpvandoorn/LeanCourse23.git | 7b0a3cf61b802764dc7baee9d9825e9c62cf9c5d | LeanCourse/Lectures/Lecture8Before.lean | Point.add_x | [144, 1] | [144, 68] | rfl | n : ℕ
a b : Point
⊢ (a + b).x = a.x + b.x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
a b : Point
⊢ (a + b).x = a.x + b.x
TACTIC:
|
https://github.com/fpvandoorn/LeanCourse23.git | 7b0a3cf61b802764dc7baee9d9825e9c62cf9c5d | LeanCourse/Lectures/Lecture8Before.lean | Point.add_y | [145, 1] | [145, 68] | rfl | n : ℕ
a b : Point
⊢ (a + b).y = a.y + b.y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
a b : Point
⊢ (a + b).y = a.y + b.y
TACTIC:
|
https://github.com/fpvandoorn/LeanCourse23.git | 7b0a3cf61b802764dc7baee9d9825e9c62cf9c5d | LeanCourse/Lectures/Lecture8Before.lean | Point.add_z | [146, 1] | [146, 68] | rfl | n : ℕ
a b : Point
⊢ (a + b).z = a.z + b.z | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
a b : Point
⊢ (a + b).z = a.z + b.z
TACTIC:
|
https://github.com/fpvandoorn/LeanCourse23.git | 7b0a3cf61b802764dc7baee9d9825e9c62cf9c5d | LeanCourse/Lectures/Lecture8Before.lean | AbelianGroup.zero_add | [303, 1] | [304, 26] | rw [g.comm, g.add_zero] | n : ℕ
g : AbelianGroup
x : g.G
⊢ add g g.zero x = x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
g : AbelianGroup
x : g.G
⊢ add g g.zero x = x
TACTIC:
|
https://github.com/fpvandoorn/LeanCourse23.git | 7b0a3cf61b802764dc7baee9d9825e9c62cf9c5d | LeanCourse/Lectures/Lecture8Before.lean | PointedFunction.comp | [487, 1] | [489, 25] | sorry | n : ℕ
X : PointedType
Y : PointedType
Z : PointedType
g : Y →. Z
f : X →. Y
⊢ (↑g ∘ ↑f) X.pt = Z.pt | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
X : PointedType
Y : PointedType
Z : PointedType
g : Y →. Z
f : X →. Y
⊢ (↑g ∘ ↑f) X.pt = Z.pt
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Lawful.lean | map_bind | [15, 1] | [19, 6] | rw [map_eq_pure_bind, bind_assoc] | m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α β γ : Type u
f : α → β
x : m α
g : β → m γ
⊢ f <$> x >>= g = x >>= g ∘ f | m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α β γ : Type u
f : α → β
x : m α
g : β → m γ
⊢ (x >>= fun x => pure (f x) >>= g) = x >>= g ∘ f | Please generate a tactic in lean4 to solve the state.
STATE:
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α β γ : Type u
f : α → β
x : m α
g : β → m γ
⊢ f <$> x >>= g = x >>= g ∘ f
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Lawful.lean | map_bind | [15, 1] | [19, 6] | apply bind_congr | m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α β γ : Type u
f : α → β
x : m α
g : β → m γ
⊢ (x >>= fun x => pure (f x) >>= g) = x >>= g ∘ f | case h
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α β γ : Type u
f : α → β
x : m α
g : β → m γ
⊢ ∀ (a : α), pure (f a) >>= g = (g ∘ f) a | Please generate a tactic in lean4 to solve the state.
STATE:
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α β γ : Type u
f : α → β
x : m α
g : β → m γ
⊢ (x >>= fun x => pure (f x) >>= g) = x >>= g ∘ f
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Lawful.lean | map_bind | [15, 1] | [19, 6] | intro a | case h
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α β γ : Type u
f : α → β
x : m α
g : β → m γ
⊢ ∀ (a : α), pure (f a) >>= g = (g ∘ f) a | case h
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α β γ : Type u
f : α → β
x : m α
g : β → m γ
a : α
⊢ pure (f a) >>= g = (g ∘ f) a | Please generate a tactic in lean4 to solve the state.
STATE:
case h
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α β γ : Type u
f : α → β
x : m α
g : β → m γ
⊢ ∀ (a : α), pure (f a) >>= g = (g ∘ f) a
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Lawful.lean | map_bind | [15, 1] | [19, 6] | rw [pure_bind] | case h
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α β γ : Type u
f : α → β
x : m α
g : β → m γ
a : α
⊢ pure (f a) >>= g = (g ∘ f) a | case h
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α β γ : Type u
f : α → β
x : m α
g : β → m γ
a : α
⊢ g (f a) = (g ∘ f) a | Please generate a tactic in lean4 to solve the state.
STATE:
case h
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α β γ : Type u
f : α → β
x : m α
g : β → m γ
a : α
⊢ pure (f a) >>= g = (g ∘ f) a
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Lawful.lean | map_bind | [15, 1] | [19, 6] | rfl | case h
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α β γ : Type u
f : α → β
x : m α
g : β → m γ
a : α
⊢ g (f a) = (g ∘ f) a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α β γ : Type u
f : α → β
x : m α
g : β → m γ
a : α
⊢ g (f a) = (g ∘ f) a
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Dijkstra.lean | DijkstraMonad.dbind_congr | [65, 1] | [75, 19] | have : wf₁ = wf₂ := by
funext a
exact (hf a).eq_param | W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ wf₂ : α → W β
x✝ : M α a✝
f₁ : (a : α) → M β (wf₁ a)
f₂ : (a : α) → M β (wf₂ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
⊢ DEq (M β) (dbind x✝ f₁) (dbind x✝ f₂) | W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ wf₂ : α → W β
x✝ : M α a✝
f₁ : (a : α) → M β (wf₁ a)
f₂ : (a : α) → M β (wf₂ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
this : wf₁ = wf₂
⊢ DEq (M β) (dbind x✝ f₁) (dbind x✝ f₂) | Please generate a tactic in lean4 to solve the state.
STATE:
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ wf₂ : α → W β
x✝ : M α a✝
f₁ : (a : α) → M β (wf₁ a)
f₂ : (a : α) → M β (wf₂ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
⊢ DEq (M β) (dbind x✝ f₁) (dbind x✝ f₂)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Dijkstra.lean | DijkstraMonad.dbind_congr | [65, 1] | [75, 19] | cases this | W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ wf₂ : α → W β
x✝ : M α a✝
f₁ : (a : α) → M β (wf₁ a)
f₂ : (a : α) → M β (wf₂ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
this : wf₁ = wf₂
⊢ DEq (M β) (dbind x✝ f₁) (dbind x✝ f₂) | case refl
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ : α → W β
x✝ : M α a✝
f₁ f₂ : (a : α) → M β (wf₁ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
⊢ DEq (M β) (dbind x✝ f₁) (dbind x✝ f₂) | Please generate a tactic in lean4 to solve the state.
STATE:
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ wf₂ : α → W β
x✝ : M α a✝
f₁ : (a : α) → M β (wf₁ a)
f₂ : (a : α) → M β (wf₂ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
this : wf₁ = wf₂
⊢ DEq (M β) (dbind x✝ f₁) (dbind x✝ f₂)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Dijkstra.lean | DijkstraMonad.dbind_congr | [65, 1] | [75, 19] | have : f₁ = f₂ := by
funext a
exact (hf a).eq_of_deq | case refl
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ : α → W β
x✝ : M α a✝
f₁ f₂ : (a : α) → M β (wf₁ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
⊢ DEq (M β) (dbind x✝ f₁) (dbind x✝ f₂) | case refl
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ : α → W β
x✝ : M α a✝
f₁ f₂ : (a : α) → M β (wf₁ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
this : f₁ = f₂
⊢ DEq (M β) (dbind x✝ f₁) (dbind x✝ f₂) | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ : α → W β
x✝ : M α a✝
f₁ f₂ : (a : α) → M β (wf₁ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
⊢ DEq (M β) (dbind x✝ f₁) (dbind x✝ f₂)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Dijkstra.lean | DijkstraMonad.dbind_congr | [65, 1] | [75, 19] | cases this | case refl
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ : α → W β
x✝ : M α a✝
f₁ f₂ : (a : α) → M β (wf₁ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
this : f₁ = f₂
⊢ DEq (M β) (dbind x✝ f₁) (dbind x✝ f₂) | case refl.refl
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ : α → W β
x✝ : M α a✝
f₁ : (a : α) → M β (wf₁ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₁ a)
⊢ DEq (M β) (dbind x✝ f₁) (dbind x✝ f₁) | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ : α → W β
x✝ : M α a✝
f₁ f₂ : (a : α) → M β (wf₁ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
this : f₁ = f₂
⊢ DEq (M β) (dbind x✝ f₁) (dbind x✝ f₂)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Dijkstra.lean | DijkstraMonad.dbind_congr | [65, 1] | [75, 19] | exact DEq.refl _ | case refl.refl
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ : α → W β
x✝ : M α a✝
f₁ : (a : α) → M β (wf₁ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₁ a)
⊢ DEq (M β) (dbind x✝ f₁) (dbind x✝ f₁) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refl.refl
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ : α → W β
x✝ : M α a✝
f₁ : (a : α) → M β (wf₁ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₁ a)
⊢ DEq (M β) (dbind x✝ f₁) (dbind x✝ f₁)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Dijkstra.lean | DijkstraMonad.dbind_congr | [65, 1] | [75, 19] | funext a | W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ wf₂ : α → W β
x✝ : M α a✝
f₁ : (a : α) → M β (wf₁ a)
f₂ : (a : α) → M β (wf₂ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
⊢ wf₁ = wf₂ | case h
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ wf₂ : α → W β
x✝ : M α a✝
f₁ : (a : α) → M β (wf₁ a)
f₂ : (a : α) → M β (wf₂ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
a : α
⊢ wf₁ a = wf₂ a | Please generate a tactic in lean4 to solve the state.
STATE:
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ wf₂ : α → W β
x✝ : M α a✝
f₁ : (a : α) → M β (wf₁ a)
f₂ : (a : α) → M β (wf₂ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
⊢ wf₁ = wf₂
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Dijkstra.lean | DijkstraMonad.dbind_congr | [65, 1] | [75, 19] | exact (hf a).eq_param | case h
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ wf₂ : α → W β
x✝ : M α a✝
f₁ : (a : α) → M β (wf₁ a)
f₂ : (a : α) → M β (wf₂ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
a : α
⊢ wf₁ a = wf₂ a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ wf₂ : α → W β
x✝ : M α a✝
f₁ : (a : α) → M β (wf₁ a)
f₂ : (a : α) → M β (wf₂ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
a : α
⊢ wf₁ a = wf₂ a
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Dijkstra.lean | DijkstraMonad.dbind_congr | [65, 1] | [75, 19] | funext a | W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ : α → W β
x✝ : M α a✝
f₁ f₂ : (a : α) → M β (wf₁ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
⊢ f₁ = f₂ | case h
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ : α → W β
x✝ : M α a✝
f₁ f₂ : (a : α) → M β (wf₁ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
a : α
⊢ f₁ a = f₂ a | Please generate a tactic in lean4 to solve the state.
STATE:
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ : α → W β
x✝ : M α a✝
f₁ f₂ : (a : α) → M β (wf₁ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
⊢ f₁ = f₂
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Dijkstra.lean | DijkstraMonad.dbind_congr | [65, 1] | [75, 19] | exact (hf a).eq_of_deq | case h
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ : α → W β
x✝ : M α a✝
f₁ f₂ : (a : α) → M β (wf₁ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
a : α
⊢ f₁ a = f₂ a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
W : Type u → Type v
inst✝¹ : Monad W
M : (α : Type u) → W α → Type w
inst✝ : DijkstraMonad W M
α β : Type u
a✝ : W α
wf₁ : α → W β
x✝ : M α a✝
f₁ f₂ : (a : α) → M β (wf₁ a)
hf : ∀ (a : α), DEq (M β) (f₁ a) (f₂ a)
a : α
⊢ f₁ a = f₂ a
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Dijkstra.lean | DijkstraMonad.Push.deq | [114, 1] | [117, 19] | cases (Eq.trans hy.symm hx) | W₁ : Type u → Type v₁
inst✝¹ : Monad W₁
W₂ : Type u → Type v₂
inst✝ : Monad W₂
F : MonadHom W₁ W₂
M : (α : Type u) → W₁ α → Type w
α : Type u
wa₂ wa₂' : W₂ α
base : W₁ α
body✝ : M α base
hx : MonadHom.app F base = wa₂
hy : MonadHom.app F base = wa₂'
⊢ DEq (Push F M α) { base := base, body := body✝, underly := hx } { base := base, body := body✝, underly := hy } | case refl
W₁ : Type u → Type v₁
inst✝¹ : Monad W₁
W₂ : Type u → Type v₂
inst✝ : Monad W₂
F : MonadHom W₁ W₂
M : (α : Type u) → W₁ α → Type w
α : Type u
wa₂ : W₂ α
base : W₁ α
body✝ : M α base
hx hy : MonadHom.app F base = wa₂
⊢ DEq (Push F M α) { base := base, body := body✝, underly := hx } { base := base, body := body✝, underly := hy } | Please generate a tactic in lean4 to solve the state.
STATE:
W₁ : Type u → Type v₁
inst✝¹ : Monad W₁
W₂ : Type u → Type v₂
inst✝ : Monad W₂
F : MonadHom W₁ W₂
M : (α : Type u) → W₁ α → Type w
α : Type u
wa₂ wa₂' : W₂ α
base : W₁ α
body✝ : M α base
hx : MonadHom.app F base = wa₂
hy : MonadHom.app F base = wa₂'
⊢ DEq (Push F M α) { base := base, body := body✝, underly := hx } { base := base, body := body✝, underly := hy }
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Dijkstra.lean | DijkstraMonad.Push.deq | [114, 1] | [117, 19] | exact DEq.refl _ | case refl
W₁ : Type u → Type v₁
inst✝¹ : Monad W₁
W₂ : Type u → Type v₂
inst✝ : Monad W₂
F : MonadHom W₁ W₂
M : (α : Type u) → W₁ α → Type w
α : Type u
wa₂ : W₂ α
base : W₁ α
body✝ : M α base
hx hy : MonadHom.app F base = wa₂
⊢ DEq (Push F M α) { base := base, body := body✝, underly := hx } { base := base, body := body✝, underly := hy } | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
W₁ : Type u → Type v₁
inst✝¹ : Monad W₁
W₂ : Type u → Type v₂
inst✝ : Monad W₂
F : MonadHom W₁ W₂
M : (α : Type u) → W₁ α → Type w
α : Type u
wa₂ : W₂ α
base : W₁ α
body✝ : M α base
hx hy : MonadHom.app F base = wa₂
⊢ DEq (Push F M α) { base := base, body := body✝, underly := hx } { base := base, body := body✝, underly := hy }
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | List.val_zipProof | [84, 1] | [90, 15] | induction as | α : Type u
p : α → Prop
as : List α
h : forAll p as
⊢ Subtype.val <$> zipProof as h = as | case nil
α : Type u
p : α → Prop
h : forAll p []
⊢ Subtype.val <$> zipProof [] h = []
case cons
α : Type u
p : α → Prop
head✝ : α
tail✝ : List α
tail_ih✝ : ∀ {h : forAll p tail✝}, Subtype.val <$> zipProof tail✝ h = tail✝
h : forAll p (head✝ :: tail✝)
⊢ Subtype.val <$> zipProof (head✝ :: tail✝) h = head✝ :: tail✝ | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u
p : α → Prop
as : List α
h : forAll p as
⊢ Subtype.val <$> zipProof as h = as
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | List.val_zipProof | [84, 1] | [90, 15] | case nil => rfl | α : Type u
p : α → Prop
h : forAll p []
⊢ Subtype.val <$> zipProof [] h = [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u
p : α → Prop
h : forAll p []
⊢ Subtype.val <$> zipProof [] h = []
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | List.val_zipProof | [84, 1] | [90, 15] | case cons a as h_ind =>
cases h with | intro ha has =>
dsimp [Functor.map, zipProof, List.map] at *
rw [h_ind] | α : Type u
p : α → Prop
a : α
as : List α
h_ind : ∀ {h : forAll p as}, Subtype.val <$> zipProof as h = as
h : forAll p (a :: as)
⊢ Subtype.val <$> zipProof (a :: as) h = a :: as | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u
p : α → Prop
a : α
as : List α
h_ind : ∀ {h : forAll p as}, Subtype.val <$> zipProof as h = as
h : forAll p (a :: as)
⊢ Subtype.val <$> zipProof (a :: as) h = a :: as
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | List.val_zipProof | [84, 1] | [90, 15] | rfl | α : Type u
p : α → Prop
h : forAll p []
⊢ Subtype.val <$> zipProof [] h = [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u
p : α → Prop
h : forAll p []
⊢ Subtype.val <$> zipProof [] h = []
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | List.val_zipProof | [84, 1] | [90, 15] | cases h with | intro ha has =>
dsimp [Functor.map, zipProof, List.map] at *
rw [h_ind] | α : Type u
p : α → Prop
a : α
as : List α
h_ind : ∀ {h : forAll p as}, Subtype.val <$> zipProof as h = as
h : forAll p (a :: as)
⊢ Subtype.val <$> zipProof (a :: as) h = a :: as | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u
p : α → Prop
a : α
as : List α
h_ind : ∀ {h : forAll p as}, Subtype.val <$> zipProof as h = as
h : forAll p (a :: as)
⊢ Subtype.val <$> zipProof (a :: as) h = a :: as
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | List.val_zipProof | [84, 1] | [90, 15] | dsimp [Functor.map, zipProof, List.map] at * | case intro
α : Type u
p : α → Prop
a : α
as : List α
h_ind : ∀ {h : forAll p as}, Subtype.val <$> zipProof as h = as
ha : p a
has : forAll p as
⊢ Subtype.val <$> zipProof (a :: as) (_ : p a ∧ forAll p as) = a :: as | case intro
α : Type u
p : α → Prop
a : α
as : List α
h_ind : ∀ {h : forAll p as}, map Subtype.val (zipProof as h) = as
ha : p a
has : forAll p as
⊢ a :: map Subtype.val (zipProof as has) = a :: as | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
α : Type u
p : α → Prop
a : α
as : List α
h_ind : ∀ {h : forAll p as}, Subtype.val <$> zipProof as h = as
ha : p a
has : forAll p as
⊢ Subtype.val <$> zipProof (a :: as) (_ : p a ∧ forAll p as) = a :: as
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | List.val_zipProof | [84, 1] | [90, 15] | rw [h_ind] | case intro
α : Type u
p : α → Prop
a : α
as : List α
h_ind : ∀ {h : forAll p as}, map Subtype.val (zipProof as h) = as
ha : p a
has : forAll p as
⊢ a :: map Subtype.val (zipProof as has) = a :: as | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
α : Type u
p : α → Prop
a : α
as : List α
h_ind : ∀ {h : forAll p as}, map Subtype.val (zipProof as h) = as
ha : p a
has : forAll p as
⊢ a :: map Subtype.val (zipProof as has) = a :: as
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | List.SatisfiesM_List_eq | [92, 1] | [102, 26] | cases h with | intro xs hx =>
cases hx
induction xs
case nil => exact True.intro
case cons a as h_ind =>
exact ⟨a.property, h_ind⟩ | α : Type u
p : α → Prop
as : List α
h : SatisfiesM p as
⊢ forAll p as | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u
p : α → Prop
as : List α
h : SatisfiesM p as
⊢ forAll p as
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | List.SatisfiesM_List_eq | [92, 1] | [102, 26] | cases hx | case intro
α : Type u
p : α → Prop
as : List α
xs : List { a // p a }
hx : Subtype.val <$> xs = as
⊢ forAll p as | case intro.refl
α : Type u
p : α → Prop
xs : List { a // p a }
⊢ forAll p (Subtype.val <$> xs) | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
α : Type u
p : α → Prop
as : List α
xs : List { a // p a }
hx : Subtype.val <$> xs = as
⊢ forAll p as
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | List.SatisfiesM_List_eq | [92, 1] | [102, 26] | induction xs | case intro.refl
α : Type u
p : α → Prop
xs : List { a // p a }
⊢ forAll p (Subtype.val <$> xs) | case intro.refl.nil
α : Type u
p : α → Prop
⊢ forAll p (Subtype.val <$> [])
case intro.refl.cons
α : Type u
p : α → Prop
head✝ : { a // p a }
tail✝ : List { a // p a }
tail_ih✝ : forAll p (Subtype.val <$> tail✝)
⊢ forAll p (Subtype.val <$> (head✝ :: tail✝)) | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.refl
α : Type u
p : α → Prop
xs : List { a // p a }
⊢ forAll p (Subtype.val <$> xs)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | List.SatisfiesM_List_eq | [92, 1] | [102, 26] | case nil => exact True.intro | α : Type u
p : α → Prop
⊢ forAll p (Subtype.val <$> []) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u
p : α → Prop
⊢ forAll p (Subtype.val <$> [])
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | List.SatisfiesM_List_eq | [92, 1] | [102, 26] | case cons a as h_ind =>
exact ⟨a.property, h_ind⟩ | α : Type u
p : α → Prop
a : { a // p a }
as : List { a // p a }
h_ind : forAll p (Subtype.val <$> as)
⊢ forAll p (Subtype.val <$> (a :: as)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u
p : α → Prop
a : { a // p a }
as : List { a // p a }
h_ind : forAll p (Subtype.val <$> as)
⊢ forAll p (Subtype.val <$> (a :: as))
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | List.SatisfiesM_List_eq | [92, 1] | [102, 26] | exact True.intro | α : Type u
p : α → Prop
⊢ forAll p (Subtype.val <$> []) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u
p : α → Prop
⊢ forAll p (Subtype.val <$> [])
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | List.SatisfiesM_List_eq | [92, 1] | [102, 26] | exact ⟨a.property, h_ind⟩ | α : Type u
p : α → Prop
a : { a // p a }
as : List { a // p a }
h_ind : forAll p (Subtype.val <$> as)
⊢ forAll p (Subtype.val <$> (a :: as)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u
p : α → Prop
a : { a // p a }
as : List { a // p a }
h_ind : forAll p (Subtype.val <$> as)
⊢ forAll p (Subtype.val <$> (a :: as))
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | List.SatisfiesM_List_eq | [92, 1] | [102, 26] | exists zipProof as h | α : Type u
p : α → Prop
as : List α
h : forAll p as
⊢ SatisfiesM p as | α : Type u
p : α → Prop
as : List α
h : forAll p as
⊢ Subtype.val <$> zipProof as h = as | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u
p : α → Prop
as : List α
h : forAll p as
⊢ SatisfiesM p as
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | List.SatisfiesM_List_eq | [92, 1] | [102, 26] | exact val_zipProof as | α : Type u
p : α → Prop
as : List α
h : forAll p as
⊢ Subtype.val <$> zipProof as h = as | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u
p : α → Prop
as : List α
h : forAll p as
⊢ Subtype.val <$> zipProof as h = as
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | ExceptT.map_eq_map_errorOrApply | [130, 1] | [137, 27] | rw [Functor.map, Applicative.toFunctor, Monad.toApplicative] | α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ f <$> x = errorOrApply f <$> x | α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ instMonadExceptT.1.1.1 f x = errorOrApply f <$> x | Please generate a tactic in lean4 to solve the state.
STATE:
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ f <$> x = errorOrApply f <$> x
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | ExceptT.map_eq_map_errorOrApply | [130, 1] | [137, 27] | unfold instMonadExceptT | α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ instMonadExceptT.1.1.1 f x = errorOrApply f <$> x | α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ Monad.mk.1.1.1 f x = errorOrApply f <$> x | Please generate a tactic in lean4 to solve the state.
STATE:
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ instMonadExceptT.1.1.1 f x = errorOrApply f <$> x
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | ExceptT.map_eq_map_errorOrApply | [130, 1] | [137, 27] | simp | α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ Monad.mk.1.1.1 f x = errorOrApply f <$> x | α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ ExceptT.map f x = errorOrApply f <$> x | Please generate a tactic in lean4 to solve the state.
STATE:
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ Monad.mk.1.1.1 f x = errorOrApply f <$> x
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | ExceptT.map_eq_map_errorOrApply | [130, 1] | [137, 27] | unfold ExceptT.map | α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ ExceptT.map f x = errorOrApply f <$> x | α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ (mk do
let a ← x
match a with
| Except.ok a => pure (Except.ok (f a))
| Except.error e => pure (Except.error e)) =
errorOrApply f <$> x | Please generate a tactic in lean4 to solve the state.
STATE:
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ ExceptT.map f x = errorOrApply f <$> x
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | ExceptT.map_eq_map_errorOrApply | [130, 1] | [137, 27] | rw [map_eq_pure_bind] | α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ (mk do
let a ← x
match a with
| Except.ok a => pure (Except.ok (f a))
| Except.error e => pure (Except.error e)) =
errorOrApply f <$> x | α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ (mk do
let a ← x
match a with
| Except.ok a => pure (Except.ok (f a))
| Except.error e => pure (Except.error e)) =
do
let a ← x
pure (errorOrApply f a) | Please generate a tactic in lean4 to solve the state.
STATE:
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ (mk do
let a ← x
match a with
| Except.ok a => pure (Except.ok (f a))
| Except.error e => pure (Except.error e)) =
errorOrApply f <$> x
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | ExceptT.map_eq_map_errorOrApply | [130, 1] | [137, 27] | apply bind_congr | α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ (mk do
let a ← x
match a with
| Except.ok a => pure (Except.ok (f a))
| Except.error e => pure (Except.error e)) =
do
let a ← x
pure (errorOrApply f a) | case h
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ ∀ (a : Except ε α),
(match a with
| Except.ok a => pure (Except.ok (f a))
| Except.error e => pure (Except.error e)) =
pure (errorOrApply f a) | Please generate a tactic in lean4 to solve the state.
STATE:
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ (mk do
let a ← x
match a with
| Except.ok a => pure (Except.ok (f a))
| Except.error e => pure (Except.error e)) =
do
let a ← x
pure (errorOrApply f a)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | ExceptT.map_eq_map_errorOrApply | [130, 1] | [137, 27] | intro e | case h
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ ∀ (a : Except ε α),
(match a with
| Except.ok a => pure (Except.ok (f a))
| Except.error e => pure (Except.error e)) =
pure (errorOrApply f a) | case h
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
e : Except ε α
⊢ (match e with
| Except.ok a => pure (Except.ok (f a))
| Except.error e => pure (Except.error e)) =
pure (errorOrApply f e) | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
⊢ ∀ (a : Except ε α),
(match a with
| Except.ok a => pure (Except.ok (f a))
| Except.error e => pure (Except.error e)) =
pure (errorOrApply f a)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | ExceptT.map_eq_map_errorOrApply | [130, 1] | [137, 27] | cases e <;> rfl | case h
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
e : Except ε α
⊢ (match e with
| Except.ok a => pure (Except.ok (f a))
| Except.error e => pure (Except.error e)) =
pure (errorOrApply f e) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
f : α → β
x : ExceptT ε m α
e : Except ε α
⊢ (match e with
| Except.ok a => pure (Except.ok (f a))
| Except.error e => pure (Except.error e)) =
pure (errorOrApply f e)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | ExceptT.errorOrApply_val | [151, 1] | [153, 18] | funext x | α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
p : α → Prop
⊢ errorOrApply Subtype.val = Subtype.val ∘ toSubtype | case h
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
p : α → Prop
x : Except ε (Subtype p)
⊢ errorOrApply Subtype.val x = (Subtype.val ∘ toSubtype) x | Please generate a tactic in lean4 to solve the state.
STATE:
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
p : α → Prop
⊢ errorOrApply Subtype.val = Subtype.val ∘ toSubtype
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | ExceptT.errorOrApply_val | [151, 1] | [153, 18] | cases x <;> rfl | case h
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
p : α → Prop
x : Except ε (Subtype p)
⊢ errorOrApply Subtype.val x = (Subtype.val ∘ toSubtype) x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
p : α → Prop
x : Except ε (Subtype p)
⊢ errorOrApply Subtype.val x = (Subtype.val ∘ toSubtype) x
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | ExceptT.from_toSubtype | [155, 1] | [157, 18] | funext x | α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
p : α → Prop
⊢ fromSubtype ∘ toSubtype = id | case h
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
p : α → Prop
x : Except ε (Subtype p)
⊢ (fromSubtype ∘ toSubtype) x = id x | Please generate a tactic in lean4 to solve the state.
STATE:
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
p : α → Prop
⊢ fromSubtype ∘ toSubtype = id
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | ExceptT.from_toSubtype | [155, 1] | [157, 18] | cases x <;> rfl | case h
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
p : α → Prop
x : Except ε (Subtype p)
⊢ (fromSubtype ∘ toSubtype) x = id x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α β ε : Type u
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
p : α → Prop
x : Except ε (Subtype p)
⊢ (fromSubtype ∘ toSubtype) x = id x
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_ReaderT_eq' | [191, 1] | [199, 35] | cases h with | intro x h =>
cases h
exists x s | m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
x : ReaderT ρ m α
h : SatisfiesM p x
s : ρ
⊢ SatisfiesM p (x s) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
x : ReaderT ρ m α
h : SatisfiesM p x
s : ρ
⊢ SatisfiesM p (x s)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_ReaderT_eq' | [191, 1] | [199, 35] | cases h | case intro
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
x✝ : ReaderT ρ m α
s : ρ
x : ReaderT ρ m { a // p a }
h : Subtype.val <$> x = x✝
⊢ SatisfiesM p (x✝ s) | case intro.refl
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
s : ρ
x : ReaderT ρ m { a // p a }
⊢ SatisfiesM p ((Subtype.val <$> x) s) | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
x✝ : ReaderT ρ m α
s : ρ
x : ReaderT ρ m { a // p a }
h : Subtype.val <$> x = x✝
⊢ SatisfiesM p (x✝ s)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_ReaderT_eq' | [191, 1] | [199, 35] | exists x s | case intro.refl
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
s : ρ
x : ReaderT ρ m { a // p a }
⊢ SatisfiesM p ((Subtype.val <$> x) s) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.refl
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
s : ρ
x : ReaderT ρ m { a // p a }
⊢ SatisfiesM p ((Subtype.val <$> x) s)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_ReaderT_eq' | [191, 1] | [199, 35] | exists λ s => SubregFunctor.ensureF (f:=m) (x s) (h s) | m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
x : ReaderT ρ m α
h : ∀ (s : ρ), SatisfiesM p (x s)
⊢ SatisfiesM p x | m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
x : ReaderT ρ m α
h : ∀ (s : ρ), SatisfiesM p (x s)
⊢ (Subtype.val <$> fun s => SubregFunctor.ensureF (x s) (_ : SatisfiesM p (x s))) = x | Please generate a tactic in lean4 to solve the state.
STATE:
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
x : ReaderT ρ m α
h : ∀ (s : ρ), SatisfiesM p (x s)
⊢ SatisfiesM p x
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_ReaderT_eq' | [191, 1] | [199, 35] | funext s | m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
x : ReaderT ρ m α
h : ∀ (s : ρ), SatisfiesM p (x s)
⊢ (Subtype.val <$> fun s => SubregFunctor.ensureF (x s) (_ : SatisfiesM p (x s))) = x | case h
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
x : ReaderT ρ m α
h : ∀ (s : ρ), SatisfiesM p (x s)
s : ρ
⊢ (Subtype.val <$> fun s => SubregFunctor.ensureF (x s) (_ : SatisfiesM p (x s))) s = x s | Please generate a tactic in lean4 to solve the state.
STATE:
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
x : ReaderT ρ m α
h : ∀ (s : ρ), SatisfiesM p (x s)
⊢ (Subtype.val <$> fun s => SubregFunctor.ensureF (x s) (_ : SatisfiesM p (x s))) = x
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_ReaderT_eq' | [191, 1] | [199, 35] | dsimp [Functor.map] | case h
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
x : ReaderT ρ m α
h : ∀ (s : ρ), SatisfiesM p (x s)
s : ρ
⊢ (Subtype.val <$> fun s => SubregFunctor.ensureF (x s) (_ : SatisfiesM p (x s))) s = x s | case h
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
x : ReaderT ρ m α
h : ∀ (s : ρ), SatisfiesM p (x s)
s : ρ
⊢ Subtype.val <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM p (x s)) = x s | Please generate a tactic in lean4 to solve the state.
STATE:
case h
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
x : ReaderT ρ m α
h : ∀ (s : ρ), SatisfiesM p (x s)
s : ρ
⊢ (Subtype.val <$> fun s => SubregFunctor.ensureF (x s) (_ : SatisfiesM p (x s))) s = x s
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_ReaderT_eq' | [191, 1] | [199, 35] | rw [SubregFunctor.val_ensureF] | case h
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
x : ReaderT ρ m α
h : ∀ (s : ρ), SatisfiesM p (x s)
s : ρ
⊢ Subtype.val <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM p (x s)) = x s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : SubregFunctor m
ρ α : Type u
p : α → Prop
x : ReaderT ρ m α
h : ∀ (s : ρ), SatisfiesM p (x s)
s : ρ
⊢ Subtype.val <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM p (x s)) = x s
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | Prod.fst_from_to_subtype | [238, 1] | [240, 15] | funext x | α σ : Type u
p : α → Prop
⊢ fstFromSubtype ∘ fstToSubtype = id | case h
α σ : Type u
p : α → Prop
x : Subtype p × σ
⊢ (fstFromSubtype ∘ fstToSubtype) x = id x | Please generate a tactic in lean4 to solve the state.
STATE:
α σ : Type u
p : α → Prop
⊢ fstFromSubtype ∘ fstToSubtype = id
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | Prod.fst_from_to_subtype | [238, 1] | [240, 15] | cases x | case h
α σ : Type u
p : α → Prop
x : Subtype p × σ
⊢ (fstFromSubtype ∘ fstToSubtype) x = id x | case h.mk
α σ : Type u
p : α → Prop
fst✝ : Subtype p
snd✝ : σ
⊢ (fstFromSubtype ∘ fstToSubtype) (fst✝, snd✝) = id (fst✝, snd✝) | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α σ : Type u
p : α → Prop
x : Subtype p × σ
⊢ (fstFromSubtype ∘ fstToSubtype) x = id x
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | Prod.fst_from_to_subtype | [238, 1] | [240, 15] | rfl | case h.mk
α σ : Type u
p : α → Prop
fst✝ : Subtype p
snd✝ : σ
⊢ (fstFromSubtype ∘ fstToSubtype) (fst✝, snd✝) = id (fst✝, snd✝) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mk
α σ : Type u
p : α → Prop
fst✝ : Subtype p
snd✝ : σ
⊢ (fstFromSubtype ∘ fstToSubtype) (fst✝, snd✝) = id (fst✝, snd✝)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | Prod.map_val_id | [242, 1] | [244, 15] | funext x | α σ : Type u
p : α → Prop
⊢ map Subtype.val id = Subtype.val ∘ fstToSubtype | case h
α σ : Type u
p : α → Prop
x : Subtype p × σ
⊢ map Subtype.val id x = (Subtype.val ∘ fstToSubtype) x | Please generate a tactic in lean4 to solve the state.
STATE:
α σ : Type u
p : α → Prop
⊢ map Subtype.val id = Subtype.val ∘ fstToSubtype
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | Prod.map_val_id | [242, 1] | [244, 15] | cases x | case h
α σ : Type u
p : α → Prop
x : Subtype p × σ
⊢ map Subtype.val id x = (Subtype.val ∘ fstToSubtype) x | case h.mk
α σ : Type u
p : α → Prop
fst✝ : Subtype p
snd✝ : σ
⊢ map Subtype.val id (fst✝, snd✝) = (Subtype.val ∘ fstToSubtype) (fst✝, snd✝) | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α σ : Type u
p : α → Prop
x : Subtype p × σ
⊢ map Subtype.val id x = (Subtype.val ∘ fstToSubtype) x
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | Prod.map_val_id | [242, 1] | [244, 15] | rfl | case h.mk
α σ : Type u
p : α → Prop
fst✝ : Subtype p
snd✝ : σ
⊢ map Subtype.val id (fst✝, snd✝) = (Subtype.val ∘ fstToSubtype) (fst✝, snd✝) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mk
α σ : Type u
p : α → Prop
fst✝ : Subtype p
snd✝ : σ
⊢ map Subtype.val id (fst✝, snd✝) = (Subtype.val ∘ fstToSubtype) (fst✝, snd✝)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_StateT_eq' | [246, 1] | [263, 41] | cases h with | intro w hw =>
cases hw
exists Prod.fstToSubtype (p:=p) <$> w s
dsimp [Functor.map, StateT.map]
rw [←comp_map, ←map_eq_pure_bind]
apply map_congr
intro x; rfl | m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : SatisfiesM p x
s : ρ
⊢ SatisfiesM (fun x => p x.fst) (x s) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : SatisfiesM p x
s : ρ
⊢ SatisfiesM (fun x => p x.fst) (x s)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_StateT_eq' | [246, 1] | [263, 41] | cases hw | case intro
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
s : ρ
w : StateT ρ m { a // p a }
hw : Subtype.val <$> w = x
⊢ SatisfiesM (fun x => p x.fst) (x s) | case intro.refl
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
⊢ SatisfiesM (fun x => p x.fst) ((Subtype.val <$> w) s) | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
s : ρ
w : StateT ρ m { a // p a }
hw : Subtype.val <$> w = x
⊢ SatisfiesM (fun x => p x.fst) (x s)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_StateT_eq' | [246, 1] | [263, 41] | exists Prod.fstToSubtype (p:=p) <$> w s | case intro.refl
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
⊢ SatisfiesM (fun x => p x.fst) ((Subtype.val <$> w) s) | case intro.refl
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
⊢ Subtype.val <$> Prod.fstToSubtype <$> w s = (Subtype.val <$> w) s | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.refl
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
⊢ SatisfiesM (fun x => p x.fst) ((Subtype.val <$> w) s)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_StateT_eq' | [246, 1] | [263, 41] | dsimp [Functor.map, StateT.map] | case intro.refl
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
⊢ Subtype.val <$> Prod.fstToSubtype <$> w s = (Subtype.val <$> w) s | case intro.refl
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
⊢ Subtype.val <$> Prod.fstToSubtype <$> w s = do
let __discr ← w s
pure (__discr.fst.val, __discr.snd) | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.refl
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
⊢ Subtype.val <$> Prod.fstToSubtype <$> w s = (Subtype.val <$> w) s
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_StateT_eq' | [246, 1] | [263, 41] | rw [←comp_map, ←map_eq_pure_bind] | case intro.refl
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
⊢ Subtype.val <$> Prod.fstToSubtype <$> w s = do
let __discr ← w s
pure (__discr.fst.val, __discr.snd) | case intro.refl
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
⊢ (Subtype.val ∘ Prod.fstToSubtype) <$> w s = (fun __discr => (__discr.fst.val, __discr.snd)) <$> w s | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.refl
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
⊢ Subtype.val <$> Prod.fstToSubtype <$> w s = do
let __discr ← w s
pure (__discr.fst.val, __discr.snd)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_StateT_eq' | [246, 1] | [263, 41] | apply map_congr | case intro.refl
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
⊢ (Subtype.val ∘ Prod.fstToSubtype) <$> w s = (fun __discr => (__discr.fst.val, __discr.snd)) <$> w s | case intro.refl.h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
⊢ ∀ (a : Subtype p × ρ), (Subtype.val ∘ Prod.fstToSubtype) a = (a.fst.val, a.snd) | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.refl
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
⊢ (Subtype.val ∘ Prod.fstToSubtype) <$> w s = (fun __discr => (__discr.fst.val, __discr.snd)) <$> w s
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_StateT_eq' | [246, 1] | [263, 41] | intro x | case intro.refl.h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
⊢ ∀ (a : Subtype p × ρ), (Subtype.val ∘ Prod.fstToSubtype) a = (a.fst.val, a.snd) | case intro.refl.h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
x : Subtype p × ρ
⊢ (Subtype.val ∘ Prod.fstToSubtype) x = (x.fst.val, x.snd) | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.refl.h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
⊢ ∀ (a : Subtype p × ρ), (Subtype.val ∘ Prod.fstToSubtype) a = (a.fst.val, a.snd)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_StateT_eq' | [246, 1] | [263, 41] | rfl | case intro.refl.h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
x : Subtype p × ρ
⊢ (Subtype.val ∘ Prod.fstToSubtype) x = (x.fst.val, x.snd) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.refl.h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
s : ρ
w : StateT ρ m { a // p a }
x : Subtype p × ρ
⊢ (Subtype.val ∘ Prod.fstToSubtype) x = (x.fst.val, x.snd)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_StateT_eq' | [246, 1] | [263, 41] | exists fun s => Prod.fstFromSubtype <$> SubregFunctor.ensureF (x s) (h s) | m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
⊢ SatisfiesM p x | m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
⊢ (Subtype.val <$> fun s =>
Prod.fstFromSubtype <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s))) =
x | Please generate a tactic in lean4 to solve the state.
STATE:
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
⊢ SatisfiesM p x
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_StateT_eq' | [246, 1] | [263, 41] | apply funext | m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
⊢ (Subtype.val <$> fun s =>
Prod.fstFromSubtype <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s))) =
x | case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
⊢ ∀ (x_1 : ρ),
(Subtype.val <$> fun s =>
Prod.fstFromSubtype <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s)))
x_1 =
x x_1 | Please generate a tactic in lean4 to solve the state.
STATE:
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
⊢ (Subtype.val <$> fun s =>
Prod.fstFromSubtype <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s))) =
x
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_StateT_eq' | [246, 1] | [263, 41] | intro s | case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
⊢ ∀ (x_1 : ρ),
(Subtype.val <$> fun s =>
Prod.fstFromSubtype <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s)))
x_1 =
x x_1 | case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
s : ρ
⊢ (Subtype.val <$> fun s =>
Prod.fstFromSubtype <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s)))
s =
x s | Please generate a tactic in lean4 to solve the state.
STATE:
case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
⊢ ∀ (x_1 : ρ),
(Subtype.val <$> fun s =>
Prod.fstFromSubtype <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s)))
x_1 =
x x_1
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_StateT_eq' | [246, 1] | [263, 41] | dsimp [Functor.map, StateT.map] | case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
s : ρ
⊢ (Subtype.val <$> fun s =>
Prod.fstFromSubtype <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s)))
s =
x s | case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
s : ρ
⊢ (do
let __discr ← Prod.fstFromSubtype <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s))
pure (__discr.fst.val, __discr.snd)) =
x s | Please generate a tactic in lean4 to solve the state.
STATE:
case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
s : ρ
⊢ (Subtype.val <$> fun s =>
Prod.fstFromSubtype <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s)))
s =
x s
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_StateT_eq' | [246, 1] | [263, 41] | rw [←map_eq_pure_bind, ←comp_map] | case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
s : ρ
⊢ (do
let __discr ← Prod.fstFromSubtype <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s))
pure (__discr.fst.val, __discr.snd)) =
x s | case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
s : ρ
⊢ ((fun __discr => (__discr.fst.val, __discr.snd)) ∘ Prod.fstFromSubtype) <$>
SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s)) =
x s | Please generate a tactic in lean4 to solve the state.
STATE:
case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
s : ρ
⊢ (do
let __discr ← Prod.fstFromSubtype <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s))
pure (__discr.fst.val, __discr.snd)) =
x s
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_StateT_eq' | [246, 1] | [263, 41] | conv =>
lhs; lhs; ext as; dsimp [Prod.map]; change as.val | case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
s : ρ
⊢ ((fun __discr => (__discr.fst.val, __discr.snd)) ∘ Prod.fstFromSubtype) <$>
SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s)) =
x s | case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
s : ρ
⊢ (fun as => as.val) <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s)) = x s | Please generate a tactic in lean4 to solve the state.
STATE:
case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
s : ρ
⊢ ((fun __discr => (__discr.fst.val, __discr.snd)) ∘ Prod.fstFromSubtype) <$>
SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s)) =
x s
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_StateT_eq' | [246, 1] | [263, 41] | conv => lhs; lhs; change Subtype.val | case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
s : ρ
⊢ (fun as => as.val) <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s)) = x s | case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
s : ρ
⊢ Subtype.val <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s)) = x s | Please generate a tactic in lean4 to solve the state.
STATE:
case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
s : ρ
⊢ (fun as => as.val) <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s)) = x s
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | SatisfiesM_StateT_eq' | [246, 1] | [263, 41] | rw [SubregFunctor.val_ensureF (x s)] | case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
s : ρ
⊢ Subtype.val <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s)) = x s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
m : Type u → Type v
inst✝² : Monad m
inst✝¹ : LawfulMonad m
inst✝ : SubregFunctor m
α ρ : Type u
p : α → Prop
x : StateT ρ m α
h : ∀ (s : ρ), SatisfiesM (fun x => p x.fst) (x s)
s : ρ
⊢ Subtype.val <$> SubregFunctor.ensureF (x s) (_ : SatisfiesM (fun x => p x.fst) (x s)) = x s
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | EStateM.SatisfiesM_EStateM_eq | [315, 1] | [329, 35] | cases hx with | intro w hw =>
cases hw
dsimp [Functor.map, EStateM.map]
cases w s <;> intro h
case ok a s' => exact (Result.ok.inj h).left ▸ a.property
case error e s' => cases h | ε σ α : Type u
p : α → Prop
x : EStateM ε σ α
hx : SatisfiesM p x
s : σ
a : α
x✝ : σ
⊢ x s = Result.ok a x✝ → p a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ε σ α : Type u
p : α → Prop
x : EStateM ε σ α
hx : SatisfiesM p x
s : σ
a : α
x✝ : σ
⊢ x s = Result.ok a x✝ → p a
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | EStateM.SatisfiesM_EStateM_eq | [315, 1] | [329, 35] | cases hw | case intro
ε σ α : Type u
p : α → Prop
x : EStateM ε σ α
s : σ
a : α
x✝ : σ
w : EStateM ε σ { a // p a }
hw : Subtype.val <$> w = x
⊢ x s = Result.ok a x✝ → p a | case intro.refl
ε σ α : Type u
p : α → Prop
s : σ
a : α
x✝ : σ
w : EStateM ε σ { a // p a }
⊢ (Subtype.val <$> w) s = Result.ok a x✝ → p a | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
ε σ α : Type u
p : α → Prop
x : EStateM ε σ α
s : σ
a : α
x✝ : σ
w : EStateM ε σ { a // p a }
hw : Subtype.val <$> w = x
⊢ x s = Result.ok a x✝ → p a
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | EStateM.SatisfiesM_EStateM_eq | [315, 1] | [329, 35] | dsimp [Functor.map, EStateM.map] | case intro.refl
ε σ α : Type u
p : α → Prop
s : σ
a : α
x✝ : σ
w : EStateM ε σ { a // p a }
⊢ (Subtype.val <$> w) s = Result.ok a x✝ → p a | case intro.refl
ε σ α : Type u
p : α → Prop
s : σ
a : α
x✝ : σ
w : EStateM ε σ { a // p a }
⊢ (match w s with
| Result.ok a s => Result.ok a.val s
| Result.error e s => Result.error e s) =
Result.ok a x✝ →
p a | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.refl
ε σ α : Type u
p : α → Prop
s : σ
a : α
x✝ : σ
w : EStateM ε σ { a // p a }
⊢ (Subtype.val <$> w) s = Result.ok a x✝ → p a
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | EStateM.SatisfiesM_EStateM_eq | [315, 1] | [329, 35] | cases w s <;> intro h | case intro.refl
ε σ α : Type u
p : α → Prop
s : σ
a : α
x✝ : σ
w : EStateM ε σ { a // p a }
⊢ (match w s with
| Result.ok a s => Result.ok a.val s
| Result.error e s => Result.error e s) =
Result.ok a x✝ →
p a | case intro.refl.ok
ε σ α : Type u
p : α → Prop
s : σ
a : α
x✝ : σ
w : EStateM ε σ { a // p a }
a✝¹ : { a // p a }
a✝ : σ
h :
(match Result.ok a✝¹ a✝ with
| Result.ok a s => Result.ok a.val s
| Result.error e s => Result.error e s) =
Result.ok a x✝
⊢ p a
case intro.refl.error
ε σ α : Type u
p : α → Prop
s : σ
a : α
x✝ : σ
w : EStateM ε σ { a // p a }
a✝¹ : ε
a✝ : σ
h :
(match Result.error a✝¹ a✝ with
| Result.ok a s => Result.ok a.val s
| Result.error e s => Result.error e s) =
Result.ok a x✝
⊢ p a | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.refl
ε σ α : Type u
p : α → Prop
s : σ
a : α
x✝ : σ
w : EStateM ε σ { a // p a }
⊢ (match w s with
| Result.ok a s => Result.ok a.val s
| Result.error e s => Result.error e s) =
Result.ok a x✝ →
p a
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | EStateM.SatisfiesM_EStateM_eq | [315, 1] | [329, 35] | case ok a s' => exact (Result.ok.inj h).left ▸ a.property | ε σ α : Type u
p : α → Prop
s : σ
a✝ : α
x✝ : σ
w : EStateM ε σ { a // p a }
a : { a // p a }
s' : σ
h :
(match Result.ok a s' with
| Result.ok a s => Result.ok a.val s
| Result.error e s => Result.error e s) =
Result.ok a✝ x✝
⊢ p a✝ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ε σ α : Type u
p : α → Prop
s : σ
a✝ : α
x✝ : σ
w : EStateM ε σ { a // p a }
a : { a // p a }
s' : σ
h :
(match Result.ok a s' with
| Result.ok a s => Result.ok a.val s
| Result.error e s => Result.error e s) =
Result.ok a✝ x✝
⊢ p a✝
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | EStateM.SatisfiesM_EStateM_eq | [315, 1] | [329, 35] | case error e s' => cases h | ε σ α : Type u
p : α → Prop
s : σ
a : α
x✝ : σ
w : EStateM ε σ { a // p a }
e : ε
s' : σ
h :
(match Result.error e s' with
| Result.ok a s => Result.ok a.val s
| Result.error e s => Result.error e s) =
Result.ok a x✝
⊢ p a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ε σ α : Type u
p : α → Prop
s : σ
a : α
x✝ : σ
w : EStateM ε σ { a // p a }
e : ε
s' : σ
h :
(match Result.error e s' with
| Result.ok a s => Result.ok a.val s
| Result.error e s => Result.error e s) =
Result.ok a x✝
⊢ p a
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | EStateM.SatisfiesM_EStateM_eq | [315, 1] | [329, 35] | exact (Result.ok.inj h).left ▸ a.property | ε σ α : Type u
p : α → Prop
s : σ
a✝ : α
x✝ : σ
w : EStateM ε σ { a // p a }
a : { a // p a }
s' : σ
h :
(match Result.ok a s' with
| Result.ok a s => Result.ok a.val s
| Result.error e s => Result.error e s) =
Result.ok a✝ x✝
⊢ p a✝ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ε σ α : Type u
p : α → Prop
s : σ
a✝ : α
x✝ : σ
w : EStateM ε σ { a // p a }
a : { a // p a }
s' : σ
h :
(match Result.ok a s' with
| Result.ok a s => Result.ok a.val s
| Result.error e s => Result.error e s) =
Result.ok a✝ x✝
⊢ p a✝
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | EStateM.SatisfiesM_EStateM_eq | [315, 1] | [329, 35] | cases h | ε σ α : Type u
p : α → Prop
s : σ
a : α
x✝ : σ
w : EStateM ε σ { a // p a }
e : ε
s' : σ
h :
(match Result.error e s' with
| Result.ok a s => Result.ok a.val s
| Result.error e s => Result.error e s) =
Result.ok a x✝
⊢ p a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ε σ α : Type u
p : α → Prop
s : σ
a : α
x✝ : σ
w : EStateM ε σ { a // p a }
e : ε
s' : σ
h :
(match Result.error e s' with
| Result.ok a s => Result.ok a.val s
| Result.error e s => Result.error e s) =
Result.ok a x✝
⊢ p a
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | EStateM.SatisfiesM_EStateM_eq | [315, 1] | [329, 35] | exists λ s => (x s).zipProof (h s) | ε σ α : Type u
p : α → Prop
x : EStateM ε σ α
h : ∀ (s : σ) (a : α) (s' : σ), x s = Result.ok a s' → p a
⊢ SatisfiesM p x | ε σ α : Type u
p : α → Prop
x : EStateM ε σ α
h : ∀ (s : σ) (a : α) (s' : σ), x s = Result.ok a s' → p a
⊢ (Subtype.val <$> fun s => Result.zipProof (x s) (_ : ∀ (a : α) (s' : σ), x s = Result.ok a s' → p a)) = x | Please generate a tactic in lean4 to solve the state.
STATE:
ε σ α : Type u
p : α → Prop
x : EStateM ε σ α
h : ∀ (s : σ) (a : α) (s' : σ), x s = Result.ok a s' → p a
⊢ SatisfiesM p x
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | EStateM.SatisfiesM_EStateM_eq | [315, 1] | [329, 35] | funext s | ε σ α : Type u
p : α → Prop
x : EStateM ε σ α
h : ∀ (s : σ) (a : α) (s' : σ), x s = Result.ok a s' → p a
⊢ (Subtype.val <$> fun s => Result.zipProof (x s) (_ : ∀ (a : α) (s' : σ), x s = Result.ok a s' → p a)) = x | case h
ε σ α : Type u
p : α → Prop
x : EStateM ε σ α
h : ∀ (s : σ) (a : α) (s' : σ), x s = Result.ok a s' → p a
s : σ
⊢ (Subtype.val <$> fun s => Result.zipProof (x s) (_ : ∀ (a : α) (s' : σ), x s = Result.ok a s' → p a)) s = x s | Please generate a tactic in lean4 to solve the state.
STATE:
ε σ α : Type u
p : α → Prop
x : EStateM ε σ α
h : ∀ (s : σ) (a : α) (s' : σ), x s = Result.ok a s' → p a
⊢ (Subtype.val <$> fun s => Result.zipProof (x s) (_ : ∀ (a : α) (s' : σ), x s = Result.ok a s' → p a)) = x
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | EStateM.SatisfiesM_EStateM_eq | [315, 1] | [329, 35] | dsimp [Functor.map, EStateM.map] | case h
ε σ α : Type u
p : α → Prop
x : EStateM ε σ α
h : ∀ (s : σ) (a : α) (s' : σ), x s = Result.ok a s' → p a
s : σ
⊢ (Subtype.val <$> fun s => Result.zipProof (x s) (_ : ∀ (a : α) (s' : σ), x s = Result.ok a s' → p a)) s = x s | case h
ε σ α : Type u
p : α → Prop
x : EStateM ε σ α
h : ∀ (s : σ) (a : α) (s' : σ), x s = Result.ok a s' → p a
s : σ
⊢ (match Result.zipProof (x s) (_ : ∀ (a : α) (s' : σ), x s = Result.ok a s' → p a) with
| Result.ok a s => Result.ok a.val s
| Result.error e s => Result.error e s) =
x s | Please generate a tactic in lean4 to solve the state.
STATE:
case h
ε σ α : Type u
p : α → Prop
x : EStateM ε σ α
h : ∀ (s : σ) (a : α) (s' : σ), x s = Result.ok a s' → p a
s : σ
⊢ (Subtype.val <$> fun s => Result.zipProof (x s) (_ : ∀ (a : α) (s' : σ), x s = Result.ok a s' → p a)) s = x s
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Functor/Subreg.lean | EStateM.SatisfiesM_EStateM_eq | [315, 1] | [329, 35] | conv =>
lhs; change Result.map (Subtype.val (p:=p)) ((x s).zipProof (h s))
rw [Result.map_val_zipProof] | case h
ε σ α : Type u
p : α → Prop
x : EStateM ε σ α
h : ∀ (s : σ) (a : α) (s' : σ), x s = Result.ok a s' → p a
s : σ
⊢ (match Result.zipProof (x s) (_ : ∀ (a : α) (s' : σ), x s = Result.ok a s' → p a) with
| Result.ok a s => Result.ok a.val s
| Result.error e s => Result.error e s) =
x s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
ε σ α : Type u
p : α → Prop
x : EStateM ε σ α
h : ∀ (s : σ) (a : α) (s' : σ), x s = Result.ok a s' → p a
s : σ
⊢ (match Result.zipProof (x s) (_ : ∀ (a : α) (s' : σ), x s = Result.ok a s' → p a) with
| Result.ok a s => Result.ok a.val s
| Result.error e s => Result.error e s) =
x s
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Reify.lean | SubtypeT.deq_of_iff | [76, 1] | [84, 17] | have : p = q := funext (λ a => propext (hpq a)) | m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α : Type u
p q : Pred α
hpq : ∀ (a : α), p a ↔ q a
⊢ ∀ (x : SubtypeT m α p), DEq (SubtypeT m α) x (weaken (_ : ∀ (a : α), p a → q a) x) | m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α : Type u
p q : Pred α
hpq : ∀ (a : α), p a ↔ q a
this : p = q
⊢ ∀ (x : SubtypeT m α p), DEq (SubtypeT m α) x (weaken (_ : ∀ (a : α), p a → q a) x) | Please generate a tactic in lean4 to solve the state.
STATE:
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α : Type u
p q : Pred α
hpq : ∀ (a : α), p a ↔ q a
⊢ ∀ (x : SubtypeT m α p), DEq (SubtypeT m α) x (weaken (_ : ∀ (a : α), p a → q a) x)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Reify.lean | SubtypeT.deq_of_iff | [76, 1] | [84, 17] | cases this | m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α : Type u
p q : Pred α
hpq : ∀ (a : α), p a ↔ q a
this : p = q
⊢ ∀ (x : SubtypeT m α p), DEq (SubtypeT m α) x (weaken (_ : ∀ (a : α), p a → q a) x) | case refl
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α : Type u
p : Pred α
hpq : ∀ (a : α), p a ↔ p a
⊢ ∀ (x : SubtypeT m α p), DEq (SubtypeT m α) x (weaken (_ : ∀ (a : α), p a → p a) x) | Please generate a tactic in lean4 to solve the state.
STATE:
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α : Type u
p q : Pred α
hpq : ∀ (a : α), p a ↔ q a
this : p = q
⊢ ∀ (x : SubtypeT m α p), DEq (SubtypeT m α) x (weaken (_ : ∀ (a : α), p a → q a) x)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Reify.lean | SubtypeT.deq_of_iff | [76, 1] | [84, 17] | intro x | case refl
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α : Type u
p : Pred α
hpq : ∀ (a : α), p a ↔ p a
⊢ ∀ (x : SubtypeT m α p), DEq (SubtypeT m α) x (weaken (_ : ∀ (a : α), p a → p a) x) | case refl
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α : Type u
p : Pred α
hpq : ∀ (a : α), p a ↔ p a
x : SubtypeT m α p
⊢ DEq (SubtypeT m α) x (weaken (_ : ∀ (a : α), p a → p a) x) | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α : Type u
p : Pred α
hpq : ∀ (a : α), p a ↔ p a
⊢ ∀ (x : SubtypeT m α p), DEq (SubtypeT m α) x (weaken (_ : ∀ (a : α), p a → p a) x)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Reify.lean | SubtypeT.deq_of_iff | [76, 1] | [84, 17] | apply DEq.deq_of_eq | case refl
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α : Type u
p : Pred α
hpq : ∀ (a : α), p a ↔ p a
x : SubtypeT m α p
⊢ DEq (SubtypeT m α) x (weaken (_ : ∀ (a : α), p a → p a) x) | case refl.a
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α : Type u
p : Pred α
hpq : ∀ (a : α), p a ↔ p a
x : SubtypeT m α p
⊢ x = weaken (_ : ∀ (a : α), p a → p a) x | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α : Type u
p : Pred α
hpq : ∀ (a : α), p a ↔ p a
x : SubtypeT m α p
⊢ DEq (SubtypeT m α) x (weaken (_ : ∀ (a : α), p a → p a) x)
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Reify.lean | SubtypeT.deq_of_iff | [76, 1] | [84, 17] | conv =>
rhs; dsimp [weaken]; congr
. skip
. ext a; change pure a | case refl.a
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α : Type u
p : Pred α
hpq : ∀ (a : α), p a ↔ p a
x : SubtypeT m α p
⊢ x = weaken (_ : ∀ (a : α), p a → p a) x | case refl.a
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α : Type u
p : Pred α
hpq : ∀ (a : α), p a ↔ p a
x : SubtypeT m α p
⊢ x = do
let a ← x
pure a | Please generate a tactic in lean4 to solve the state.
STATE:
case refl.a
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α : Type u
p : Pred α
hpq : ∀ (a : α), p a ↔ p a
x : SubtypeT m α p
⊢ x = weaken (_ : ∀ (a : α), p a → p a) x
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Reify.lean | SubtypeT.deq_of_iff | [76, 1] | [84, 17] | rw [bind_pure] | case refl.a
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α : Type u
p : Pred α
hpq : ∀ (a : α), p a ↔ p a
x : SubtypeT m α p
⊢ x = do
let a ← x
pure a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refl.a
m : Type u → Type v
inst✝¹ : Monad m
inst✝ : LawfulMonad m
α : Type u
p : Pred α
hpq : ∀ (a : α), p a ↔ p a
x : SubtypeT m α p
⊢ x = do
let a ← x
pure a
TACTIC:
|
https://github.com/Junology/dijkstra.git | 81543f27ea34811910c10871ecf7e6243f952b19 | Dijkstra/Control/Monad/Hom.lean | MonadHom.ext | [43, 1] | [46, 12] | apply MonadHom.eq (m:=m) | m : Type u → Type v
inst✝¹ : Monad m
n : Type u → Type w
inst✝ : Monad n
F G : MonadHom m n
h : ∀ {α : Type u} (x : m α), app F x = app G x
⊢ F = G | m : Type u → Type v
inst✝¹ : Monad m
n : Type u → Type w
inst✝ : Monad n
F G : MonadHom m n
h : ∀ {α : Type u} (x : m α), app F x = app G x
⊢ F.app = G.app | Please generate a tactic in lean4 to solve the state.
STATE:
m : Type u → Type v
inst✝¹ : Monad m
n : Type u → Type w
inst✝ : Monad n
F G : MonadHom m n
h : ∀ {α : Type u} (x : m α), app F x = app G x
⊢ F = G
TACTIC:
|
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