Theorems · Theorem · order theory

IsOrderedModule.of_smul_one_mono

∀ {α : Type u_1} {β : Type u_2} [inst : Zero α] [inst_1 : Zero β] [inst_2 : SMulWithZero α β] [inst_3 : Preorder α]
  [inst_4 : Preorder β] [inst_5 : MulOneClass β] [PosMulMono β] [MulPosMono β] [IsScalarTower α β β],
  (Monotone fun x => x • 1) → IsOrderedModule α β

Defined in

Mathlib.Algebra.Order.Module.Defs

Cited by

2 results in Mathlib

Foundations

Depth 8 from the axioms · uses propext

Assumes

ZeroZeroSMulWithZeroPreorderPreorderMulOneClassPosMulMonoMulPosMonoIsScalarTower