Theorems · Theorem · order theory

Function.Injective.mulPosStrictMono

∀ {α : Type u_1} [inst : Mul α] [inst_1 : Zero α] [inst_2 : Preorder α] [MulPosStrictMono α] {β : Type u_2}
  [inst_4 : Zero β] [inst_5 : Mul β] [inst_6 : Preorder β] (f : β → α),
  f 0 = 0 → (∀ (x y : β), f (x * y) = f x * f y) → (∀ {x y : β}, f x < f y ↔ x < y) → MulPosStrictMono β

Pullback MulPosStrictMono.

Defined in

Mathlib.Algebra.Order.GroupWithZero.Defs

Cited by

0 results in Mathlib

Foundations

Depth 6 from the axioms · uses propext

Assumes

MulZeroPreorderMulPosStrictMonoZeroMulPreorder