Theorems · Definition · order theory

OrderIso.smulRight

{α : Type u_1} →
  {β : Type u_2} →
    [inst : GroupWithZero α] →
      [inst_1 : Preorder α] →
        [inst_2 : Preorder β] →
          [inst_3 : MulAction α β] → [PosSMulMono α β] → [PosSMulReflectLE α β] → {a : α} → 0 < a → β ≃o β

Right scalar multiplication as an order isomorphism.

Defined in

Mathlib.Algebra.Order.Module.Defs

Cited by

8 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupWithZeroPreorderPreorderMulActionPosSMulMonoPosSMulReflectLE