Mathlib Map

Theorems · Theorem · order theory

StrictMono.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], StrictMono f → 0 < a → StrictMono fun x => a * f x
Defined in
Mathlib.Algebra.Order.GroupWithZero.Basic
Cited by
2 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.

Real.strictMono_rpow_of_base_gt_one · cited by 2Real.strictMono_rpow_of_b…Even.strictConvexOn_pow · cited by 0Even.strictConvexOn_powPreorder · cited by 7952PreorderPartialOrder · cited by 6410PartialOrderStrictMono · cited by 706StrictMonoMonoidWithZero · cited by 456MonoidWithZeroPosMulStrictMono · cited by 151PosMulStrictMonoStrictMono.comp · cited by 36StrictMono.compstrictMono_mul_left_of_pos · cited by 3strictMono_mul_left_of_posStrictMono.const_mulCITED BYCITES

Cites7

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

Cited by2

Results whose statement or proof uses this declaration.