Theorems · Theorem · order theory
Monotone.mul_const
∀ {α : Type u_1} {M₀ : Type u_2} [inst : MonoidWithZero M₀] [inst_1 : Preorder M₀] {a : M₀} [inst_2 : Preorder α]
{f : α → M₀} [MulPosMono M₀], Monotone f → 0 ≤ a → Monotone fun x => f x * a- Cited by
- 2 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
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.
- Preorderstatement and proof · cited by 7,952
- Monotonestatement and proof · cited by 1,397
- MonoidWithZerostatement and proof · cited by 456
- MulPosMonostatement and proof · cited by 128
- Monotone.compproof · cited by 67
- monotone_mul_right_of_nonnegproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- AbsolutelyContinuousOnInterval.boundedVariationOnproof · cited by 2
- ProbabilityTheory.Kernel.IsProper.lintegral_mulproof · cited by 0