Theorems · Theorem · order theory
mul_neg_of_pos_of_neg
∀ {α : Type u_1} [inst : MulZeroClass α] {a b : α} [inst_1 : Preorder α] [PosMulStrictMono α], 0 < a → b < 0 → a * b < 0- Cited by
- 13 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClassstatement and proof · cited by 232
- PosMulStrictMonostatement and proof · cited by 151
- mul_lt_mul_of_pos_leftproof · cited by 71
Cited by13
Results whose statement or proof uses this declaration.
- nonneg_of_mul_nonneg_rightproof · cited by 8
- UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_centerproof · cited by 5
- Odd.pow_neg_iffproof · cited by 3
- Odd.zpow_neg_iffproof · cited by 3
- eq_zero_of_sameRay_neg_smul_rightproof · cited by 2
- IsUnifLocDoublingMeasure.eventually_measure_mul_le_scalingConstantOf_mulproof · cited by 2
- UpperHalfPlane.σ_mulproof · cited by 1
- nonneg_and_nonneg_or_nonpos_and_nonpos_of_mul_nonnegproof · cited by 1
- NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_topproof · cited by 0
- Asymptotics.IsEquivalent.eventually_negproof · cited by 0
- div_neg_of_pos_of_negproof · cited by 0
- Real.mul_log_negproof · cited by 0