Theorems · Theorem · order theory
nonneg_of_mul_nonneg_left
∀ {R : Type u} [inst : Semiring R] [inst_1 : LinearOrder R] {a b : R} [MulPosStrictMono R], 0 ≤ a * b → 0 < b → 0 ≤ a- Cited by
- 3 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.
Cites6
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
- le_of_not_gtproof · cited by 430
- LT.lt.not_geproof · cited by 305
- MulPosStrictMonostatement and proof · cited by 94
- mul_neg_of_neg_of_posproof · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- mul_nonneg_iff_left_nonneg_of_posproof · cited by 2
- EuclideanGeometry.dist_mul_of_eq_angle_of_dist_mulproof · cited by 1
- Complex.exp_eq_one_iff_of_im_nonnegproof · cited by 0