Theorems · Theorem · order theory
div_lt_iff_of_neg
∀ {α : Type u_2} [inst : Field α] [inst_1 : PartialOrder α] [PosMulReflectLT α] [IsStrictOrderedRing α] {a b c : α},
c < 0 → (b / c < a ↔ a * c < b)- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 46 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
- LT.lt.neproof · cited by 872
- PosMulReflectLTstatement and proof · cited by 278
- ne_of_ltproof · cited by 203
- div_mul_cancel₀proof · cited by 122
- mul_inv_cancel_right₀proof · cited by 30
- division_defproof · cited by 21
- inv_lt_zero'proof · cited by 11
- mul_lt_mul_of_neg_rightproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- div_lt_div_right_of_negproof · cited by 4
- Set.preimage_mul_const_Iio_of_negproof · cited by 3
- inv_lt_inv_of_negproof · cited by 3
- div_lt_one_of_negproof · cited by 1
- FloorSemiring.tendsto_mul_pow_div_factorial_sub_atTopproof · cited by 1
- div_lt_iff_of_neg'proof · cited by 1
- arithGeom_strictMonoproof · cited by 1