Theorems · Theorem · order theory
div_neg_of_neg_of_pos
∀ {α : Type u_2} [inst : Field α] [inst_1 : PartialOrder α] [PosMulReflectLT α] [IsStrictOrderedRing α] {a b : α},
a < 0 → 0 < b → a / b < 0- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- div_eq_mul_invproof · cited by 715
- PosMulReflectLTstatement and proof · cited by 278
- inv_posproof · cited by 124
- mul_neg_of_neg_of_posproof · cited by 13
Cited by9
Results whose statement or proof uses this declaration.
- Sbtw.angle₁₂₃_eq_piproof · cited by 6
- Function.Periodic.invQParam_tendstoproof · cited by 3
- Real.Gamma_three_div_two_lt_oneproof · cited by 2
- Function.Periodic.im_invQParam_pos_of_norm_lt_oneproof · cited by 2
- AffineSubspace.setOfPred_sOppSide_eq_image2proof · cited by 2
- AffineSubspace.setOfPred_wOppSide_eq_image2proof · cited by 2
- strictConcaveOn_sqrt_mul_log_Ioiproof · cited by 1
- Real.strictConcaveOn_qaryEntropyproof · cited by 1
- Real.cos_pi_div_fiveproof · cited by 0