Theorems · Theorem · order theory
div_neg_of_pos_of_neg
∀ {α : Type u_2} [inst : Field α] [inst_1 : PartialOrder α] [PosMulReflectLT α] [IsStrictOrderedRing α] {a b : α},
0 < a → b < 0 → a / b < 0- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- mul_neg_of_pos_of_negproof · cited by 13
- inv_lt_zero'proof · cited by 11
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