Theorems · Theorem · order theory

pos_and_pos_or_neg_and_neg_of_smul_pos

∀ {α : Type u_1} {β : Type u_2} {a : α} {b : β} [inst : Zero α] [inst_1 : Zero β] [inst_2 : SMulWithZero α β]
  [inst_3 : LinearOrder α] [inst_4 : LinearOrder β] [PosSMulMono α β] [SMulPosMono α β],
  0 < a • b → 0 < a ∧ 0 < b ∨ a < 0 ∧ b < 0

Defined in

Mathlib.Algebra.Order.Module.Defs

Cited by

2 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext

Assumes

ZeroZeroSMulWithZeroLinearOrderLinearOrderPosSMulMonoSMulPosMono