Theorems · Theorem · order theory

smul_le_smul_iff_of_neg_left

∀ {α : Type u_1} {β : Type u_2} {a : α} {b₁ b₂ : β} [inst : Ring α] [inst_1 : PartialOrder α] [IsOrderedRing α]
  [inst_3 : AddCommGroup β] [inst_4 : PartialOrder β] [IsOrderedAddMonoid β] [inst_6 : Module α β] [PosSMulMono α β]
  [PosSMulReflectLE α β], a < 0 → (a • b₁ ≤ a • b₂ ↔ b₂ ≤ b₁)

Defined in

Mathlib.Algebra.Order.Module.Defs

Cited by

2 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Quot.sound

Assumes

RingPartialOrderIsOrderedRingAddCommGroupPartialOrderIsOrderedAddMonoidModulePosSMulMonoPosSMulReflectLE