Theorems · Theorem · order theory

StrictMono.mul_monotone

∀ {α : Type u_1} {M₀ : Type u_2} [inst : MonoidWithZero M₀] [inst_1 : PartialOrder M₀] [inst_2 : Preorder α]
  {f g : α → M₀} [PosMulMono M₀] [MulPosStrictMono M₀],
  StrictMono f → Monotone g → (∀ (x : α), 0 ≤ f x) → (∀ (x : α), 0 < g x) → StrictMono (f * g)

Defined in

Mathlib.Algebra.Order.GroupWithZero.Basic

Cited by

0 results in Mathlib

Foundations

Depth 10 from the axioms · uses no axioms

Assumes

MonoidWithZeroPartialOrderPreorderPosMulMonoMulPosStrictMono