Theorems · Theorem · order theory

Monotone.comp_monotoneOn

∀ {α : Type u} {β : Type v} {γ : Type w} [inst : Preorder α] [inst_1 : Preorder β] [inst_2 : Preorder γ] {g : β → γ}
  {f : α → β} {s : Set α}, Monotone g → MonotoneOn f s → MonotoneOn (g ∘ f) s

Defined in

Mathlib.Order.Monotone.Defs

Cited by

6 results in Mathlib

Foundations

Depth 5 from the axioms · uses no axioms

Assumes

PreorderPreorderPreorder