Theorems · Theorem · order theory
inv_lt_inv_of_neg
∀ {α : Type u_2} [inst : Field α] [inst_1 : PartialOrder α] [PosMulReflectLT α] [IsStrictOrderedRing α] {a b : α},
a < 0 → b < 0 → (a⁻¹ < b⁻¹ ↔ b < a)- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- one_mulproof · cited by 2,841
- IsStrictOrderedRingstatement and proof · cited by 2,490
- mul_commproof · cited by 2,262
- one_divproof · cited by 624
- PosMulReflectLTstatement and proof · cited by 278
- division_defproof · cited by 21
- div_lt_iff_of_negproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- lt_inv_of_negproof · cited by 2
- inv_lt_of_negproof · cited by 1
- one_div_lt_one_div_of_negproof · cited by 0