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Theorems · Theorem · order theory

neg_of_mul_pos_right

∀ {α : Type u_1} [inst : MulZeroClass α] {a b : α} [inst_1 : LinearOrder α] [PosMulMono α] [MulPosMono α],
  0 < a * b → a ≤ 0 → b < 0
Defined in
Mathlib.Algebra.Order.GroupWithZero.Basic
Cited by
2 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext
Assumes
MulZeroClassLinearOrderPosMulMonoMulPosMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

neg_iff_neg_of_mul_pos · cited by 0neg_iff_neg_of_mul_posUnits.inv_neg · cited by 0Units.inv_negLinearOrder · cited by 8572LinearOrderLT.lt.not_ge · cited by 305lt.not_geMulZeroClass · cited by 232MulZeroClassPosMulMono · cited by 165PosMulMonoMulPosMono · cited by 128MulPosMonopos_and_pos_or_neg_and_neg_of_mul_pos · cited by 3pos_and_pos_or_neg_and_ne…neg_of_mul_pos_rightCITED BYCITES

Cites6

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Cited by2

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