Mathlib Map

Theorems · Theorem · order theory

StrictAnti.const_mul

∀ {α : Type u_1} {M₀ : Type u_2} [inst : MonoidWithZero M₀] [inst_1 : PartialOrder M₀] {a : M₀} [inst_2 : Preorder α]
  {f : α → M₀} [PosMulStrictMono M₀], StrictAnti f → 0 < a → StrictAnti fun x => a * f x
Defined in
Mathlib.Algebra.Order.GroupWithZero.Basic
Cited by
1 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
MonoidWithZeroPartialOrderPreorderPosMulStrictMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AkraBazziRecurrence.strictAnti_sumCoeffsExp · cited by 1AkraBazziRecurrence.stric…Preorder · cited by 7952PreorderPartialOrder · cited by 6410PartialOrderMonoidWithZero · cited by 456MonoidWithZeroStrictAnti · cited by 204StrictAntiPosMulStrictMono · cited by 151PosMulStrictMonoStrictMono.comp_strictAnti · cited by 6StrictMono.comp_strictAntistrictMono_mul_left_of_pos · cited by 3strictMono_mul_left_of_posStrictAnti.const_mulCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.