f8866dcc59
This PR fixes a bug in `grind?`. The suggestion using the `grind` interactive mode was dropping the configuration options provided by the user. In the following account, the third suggestion was dropping the `-reducible` option. ```lean /-- info: Try these: [apply] grind -reducible only [Equiv.congr_fun, #5103] [apply] grind -reducible only [Equiv.congr_fun] [apply] grind -reducible => cases #5103 <;> instantiate only [Equiv.congr_fun] -/ example : (Equiv.sigmaCongrRight e).trans (Equiv.sigmaEquivProd α₁ β₂) = (Equiv.sigmaEquivProd α₁ β₁).trans (prodCongrRight e) := by grind? -reducible [Equiv.congr_fun] ```
62 lines
2.1 KiB
Text
62 lines
2.1 KiB
Text
variable {α β γ : Type}
|
||
|
||
structure Equiv (α β : Type) where
|
||
toFun : α → β
|
||
invFun : β → α
|
||
|
||
infixl:25 " ≃ " => Equiv
|
||
|
||
namespace Equiv
|
||
|
||
instance : CoeFun (α ≃ β) (fun _ => α → β) := ⟨toFun⟩
|
||
|
||
@[ext, grind ext] theorem ext {f g : Equiv α β} (H : ∀ x, f x = g x) : f = g := sorry
|
||
|
||
theorem congr_fun {f g : Equiv α β} (h : f = g) (x : α) : f x = g x := by rw [h]
|
||
|
||
def symm (e : α ≃ β) : β ≃ α := ⟨e.invFun, e.toFun⟩
|
||
|
||
def trans (e₁ : α ≃ β) (e₂ : β ≃ γ) : α ≃ γ := ⟨e₂ ∘ e₁, e₁.symm ∘ e₂.symm⟩
|
||
|
||
def sigmaCongrRight {α : Type} {β₁ β₂ : α → Type} (F : ∀ a, β₁ a ≃ β₂ a) : (Σ a, β₁ a) ≃ Σ a, β₂ a where
|
||
toFun a := ⟨a.1, F a.1 a.2⟩
|
||
invFun a := ⟨a.1, (F a.1).symm a.2⟩
|
||
|
||
def sigmaEquivProd (α β : Type) : (Σ _ : α, β) ≃ α × β where
|
||
toFun a := ⟨a.1, a.2⟩
|
||
invFun a := ⟨a.1, a.2⟩
|
||
|
||
end Equiv
|
||
|
||
variable {α₁ β₁ β₂ : Type} (e : α₁ → β₁ ≃ β₂)
|
||
|
||
def prodCongrRight : α₁ × β₁ ≃ α₁ × β₂ where
|
||
toFun ab := ⟨ab.1, e ab.1 ab.2⟩
|
||
invFun ab := ⟨ab.1, (e ab.1).symm ab.2⟩
|
||
|
||
example :
|
||
(Equiv.sigmaCongrRight e).trans (Equiv.sigmaEquivProd α₁ β₂)
|
||
= (Equiv.sigmaEquivProd α₁ β₁).trans (prodCongrRight e) := by
|
||
grind -reducible only [Equiv.congr_fun]
|
||
|
||
example :
|
||
(Equiv.sigmaCongrRight e).trans (Equiv.sigmaEquivProd α₁ β₂)
|
||
= (Equiv.sigmaEquivProd α₁ β₁).trans (prodCongrRight e) := by
|
||
grind -reducible only => finish only [Equiv.congr_fun]
|
||
|
||
example :
|
||
(Equiv.sigmaCongrRight e).trans (Equiv.sigmaEquivProd α₁ β₂)
|
||
= (Equiv.sigmaEquivProd α₁ β₁).trans (prodCongrRight e) := by
|
||
grind -reducible => cases #5103 <;> instantiate only [Equiv.congr_fun]
|
||
|
||
/--
|
||
info: Try these:
|
||
[apply] grind -reducible only [Equiv.congr_fun, #5103]
|
||
[apply] grind -reducible only [Equiv.congr_fun]
|
||
[apply] grind -reducible => cases #5103 <;> instantiate only [Equiv.congr_fun]
|
||
-/
|
||
#guard_msgs in
|
||
example :
|
||
(Equiv.sigmaCongrRight e).trans (Equiv.sigmaEquivProd α₁ β₂)
|
||
= (Equiv.sigmaEquivProd α₁ β₁).trans (prodCongrRight e) := by
|
||
grind? -reducible [Equiv.congr_fun]
|