Theorems · Theorem · order theory
mul_le_mul_of_nonneg_of_nonpos
∀ {R : Type u} [inst : Semiring R] [inst_1 : Preorder R] {a b c d : R} [ExistsAddOfLE R] [MulPosMono R] [PosMulMono R]
[AddRightMono R] [AddRightReflectLE R], c ≤ a → b ≤ d → 0 ≤ c → b ≤ 0 → a * b ≤ c * d- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Preorderstatement and proof · cited by 7,952
- LE.le.transproof · cited by 3,151
- AddRightMonostatement and proof · cited by 367
- mul_le_mul_of_nonneg_leftproof · cited by 361
- ExistsAddOfLEstatement and proof · cited by 330
- PosMulMonostatement and proof · cited by 165
- MulPosMonostatement and proof · cited by 128
- AddRightReflectLEstatement and proof · cited by 53
- mul_le_mul_of_nonpos_rightproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- Monotone.mul_antitoneproof · cited by 0