Theorems · Theorem · order theory

smul_inv_lt_iff_of_neg

∀ {𝕜 : Type u_1} {G : Type u_2} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜]
  [inst_3 : AddCommGroup G] [inst_4 : PartialOrder G] [IsOrderedAddMonoid G] [inst_6 : Module 𝕜 G] {a : 𝕜} {b₁ b₂ : G}
  [PosSMulStrictMono 𝕜 G], a < 0 → (b₁ < a⁻¹ • b₂ ↔ b₂ < a • b₁)

Defined in

Mathlib.Algebra.Order.Module.Field

Cited by

0 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingAddCommGroupPartialOrderIsOrderedAddMonoidModulePosSMulStrictMono