Theorems · Theorem · order theory

StrictMonoOn.dual

∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β} {s : Set α},
  StrictMonoOn f s → StrictMonoOn (⇑OrderDual.toDual ∘ f ∘ ⇑OrderDual.ofDual) s

Alias of the reverse direction of strictMonoOn_dual_iff.

Defined in

Mathlib.Order.Monotone.Basic

Cited by

6 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Quot.sound

Assumes

PreorderPreorder