Theorems · Theorem · order theory
antitone_mul_left
∀ {R : Type u} [inst : Semiring R] [inst_1 : Preorder R] [ExistsAddOfLE R] [PosMulMono R] [AddRightMono R]
[AddRightReflectLE R] {a : R}, a ≤ 0 → Antitone fun x => a * x- Cited by
- 3 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.
Cites8
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
- Antitonestatement · cited by 563
- AddRightMonostatement and proof · cited by 367
- ExistsAddOfLEstatement and proof · cited by 330
- PosMulMonostatement and proof · cited by 165
- AddRightReflectLEstatement and proof · cited by 53
- mul_le_mul_of_nonpos_leftproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- Monotone.const_mul_of_nonposproof · cited by 0
- Antitone.const_mul_of_nonposproof · cited by 0
- lt_of_mul_lt_mul_of_nonpos_leftproof · cited by 0