Theorems · Theorem · order theory

bddAbove_smul_iff_of_pos

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] [inst_2 : GroupWithZero α] [inst_3 : Zero β]
  [inst_4 : MulActionWithZero α β] [PosSMulMono α β] [PosSMulReflectLE α β] {s : Set β} {a : α},
  0 < a → (BddAbove (a • s) ↔ BddAbove s)

Defined in

Mathlib.Algebra.Order.Module.Pointwise

Cited by

1 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderPreorderGroupWithZeroZeroMulActionWithZeroPosSMulMonoPosSMulReflectLE