Theorems · Theorem · order theory

StrictMonoOn.add_monotone

∀ {α : Type u_1} {β : Type u_2} [inst : Add α] [inst_1 : Preorder α] [inst_2 : Preorder β] {f g : β → α} {s : Set β}
  [AddLeftMono α] [AddRightStrictMono α], StrictMonoOn f s → MonotoneOn g s → StrictMonoOn (fun x => f x + g x) s

The sum of a strictly monotone function and a monotone function is strictly monotone.

Defined in

Mathlib.Algebra.Order.Monoid.Unbundled.Basic

Cited by

2 results in Mathlib

Foundations

Depth 8 from the axioms · uses no axioms

Assumes

AddPreorderPreorderAddLeftMonoAddRightStrictMono