Theorems · Theorem · order theory
nonpos_of_mul_nonneg_right
∀ {R : Type u} [inst : Semiring R] [inst_1 : LinearOrder R] {a b : R} [MulPosStrictMono R], 0 ≤ a * b → a < 0 → b ≤ 0- Cited by
- 1 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 by1
Results whose statement or proof uses this declaration.
- exists_hasDerivWithinAt_eq_of_gt_of_ltproof · cited by 2