Really nice solution to cjq2, thanks Youwen!

Changes

1 changed files (+3/-13)

• BinOp.lean
  • @@ -6,19 +6,9 @@ example (f : α → α → α) l r (hl : ∀ x, f l x = x) (hr : ∀ x, f x r =
    have : f l r = l := by grind grind - example [Nonempty α] (f : α → α → α) (h : ∀ x y, ∃ z, f x z = y ∧ ∀ z', f x z = f x z' → z = z') : ∃ g : α → α → α, ∀ x y, f x (g x y) = y ∧ g x (f x y) = y := by - let g x y := (f x).invFun y - use g - intro x y - constructor - · have h₁ x : (f x).Surjective := by - intro y - grind [h x y] - apply Function.rightInverse_invFun (h₁ x) - · have h₁ x : (f x).Injective := by - intro a b - grind [h x (f x a)] - apply Function.leftInverse_invFun (h₁ x) + example (f : α → α → α) (h : ∀ x y, ∃ z, f x z = y ∧ ∀ z', f x z = f x z' → z = z') : ∃ g : α → α → α, ∀ x y, f x (g x y) = y ∧ g x (f x y) = y := by + use fun x y ↦ Classical.choose <| h x y + grind example (f g : α → α → α) i j (hid : ∀ x, f i x = x ∧ f x i = x ∧ g j x = x ∧ g x j = x) (h : ∀ x y z w, f (g x y) (g z w) = g (f x z) (f y w)) : f = g := by have : i = j := by grind [hid j]