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doc(order/monotone): fix 2 typos (#10377)
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urkud committed Nov 18, 2021
1 parent 2f3b185 commit 198ed6b
Showing 1 changed file with 2 additions and 2 deletions.
4 changes: 2 additions & 2 deletions src/order/monotone.lean
Expand Up @@ -70,11 +70,11 @@ def monotone (f : α → β) : Prop := ∀ ⦃a b⦄, a ≤ b → f a ≤ f b
/-- A function `f` is antitone if `a ≤ b` implies `f b ≤ f a`. -/
def antitone (f : α → β) : Prop := ∀ ⦃a b⦄, a ≤ b → f b ≤ f a

/-- A function `f` is monotone on `s` if, for all `a, b ∈ s`, `a ≤ b` implies `f b ≤ f a`. -/
/-- A function `f` is monotone on `s` if, for all `a, b ∈ s`, `a ≤ b` implies `f a ≤ f b`. -/
def monotone_on (f : α → β) (s : set α) : Prop :=
∀ ⦃a⦄ (ha : a ∈ s) ⦃b⦄ (hb : b ∈ s), a ≤ b → f a ≤ f b

/-- A function `f` is antitone on `s` if, for all `a, b ∈ s`, `a ≤ b` implies `f a ≤ f b`. -/
/-- A function `f` is antitone on `s` if, for all `a, b ∈ s`, `a ≤ b` implies `f b ≤ f a`. -/
def antitone_on (f : α → β) (s : set α) : Prop :=
∀ ⦃a⦄ (ha : a ∈ s) ⦃b⦄ (hb : b ∈ s), a ≤ b → f b ≤ f a

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