Theorems · Theorem · order theory
monotone_mul_left_of_nonneg
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] [inst_1 : Preorder M₀] {a : M₀} [PosMulMono M₀],
0 ≤ a → Monotone fun x => a * x- Cited by
- 8 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Monotonestatement · cited by 1,397
- MonoidWithZerostatement and proof · cited by 456
- mul_le_mul_of_nonneg_leftproof · cited by 361
- PosMulMonostatement and proof · cited by 165
Cited by8
Results whose statement or proof uses this declaration.
- mul_max_of_nonnegproof · cited by 10
- geom_leproof · cited by 2
- mul_min_of_nonnegproof · cited by 2
- le_geomproof · cited by 1
- lt_geomproof · cited by 0
- geom_ltproof · cited by 0
- Monotone.const_mulproof · cited by 0
- Antitone.const_mulproof · cited by 0