Theorems · Theorem · order theory
le_div_iff_of_neg
∀ {α : Type u_2} [inst : Field α] [inst_1 : PartialOrder α] [PosMulReflectLT α] [IsStrictOrderedRing α] {a b c : α},
c < 0 → (a ≤ b / c ↔ b ≤ a * c)- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 3 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.
Cites11
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
- neg_negproof · cited by 960
- neg_mulproof · cited by 654
- mul_negproof · cited by 590
- PosMulReflectLTstatement and proof · cited by 278
- div_le_iff₀proof · cited by 97
- neg_posproof · cited by 74
- div_negproof · cited by 22
- le_negproof · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- Set.preimage_mul_const_Ici_of_negproof · cited by 3
- one_le_div_of_negproof · cited by 0
- le_div_iff_of_neg'proof · cited by 0