Theorems · Theorem · order theory
mul_neg_of_neg_of_pos
∀ {α : Type u_1} [inst : MulZeroClass α] {a b : α} [inst_1 : Preorder α] [MulPosStrictMono α], a < 0 → 0 < b → 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.zero_mulproof · cited by 1,625
- MulZeroClassstatement and proof · cited by 232
- MulPosStrictMonostatement and proof · cited by 94
- mul_lt_mul_of_pos_rightproof · cited by 54
Cited by13
Results whose statement or proof uses this declaration.
- div_neg_of_neg_of_posproof · cited by 9
- nonneg_of_mul_nonneg_leftproof · cited by 3
- MeasureTheory.ae_nonneg_of_forall_setIntegral_nonnegproof · cited by 3
- PhragmenLindelof.horizontal_stripproof · cited by 3
- summable_of_ratio_norm_eventually_leproof · cited by 2
- ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self'proof · cited by 1
- norm_jacobiTheta_sub_one_leproof · cited by 1
- norm_exp_mul_sq_leproof · cited by 1
- nonpos_of_mul_nonneg_rightproof · cited by 1
- geom_sum_pos_and_lt_oneproof · cited by 1
- UpperHalfPlane.σ_mulproof · cited by 1
- nonneg_and_nonneg_or_nonpos_and_nonpos_of_mul_nonnegproof · cited by 1