Theorems · Theorem · order theory
pos_of_mul_neg_left
∀ {R : Type u} [inst : Semiring R] [inst_1 : LinearOrder R] [ExistsAddOfLE R] [MulPosMono R] [AddRightMono R]
[AddRightReflectLE R] {a b : R}, a * b < 0 → b ≤ 0 → 0 < a- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
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.
- Semiringstatement and proof · cited by 13,802
- LinearOrderstatement and proof · cited by 8,572
- lt_of_not_geproof · cited by 374
- AddRightMonostatement and proof · cited by 367
- ExistsAddOfLEstatement and proof · cited by 330
- LE.le.not_gtproof · cited by 189
- MulPosMonostatement and proof · cited by 128
- AddRightReflectLEstatement and proof · cited by 53
- mul_nonneg_of_nonpos_of_nonposproof · cited by 45
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.cyclotomic_posproof · cited by 1
- pos_iff_neg_of_mul_negproof · cited by 0