Mathlib Map

Theorems · Theorem · order theory

Monotone.const_add

∀ {α : Type u_1} {β : Type u_2} [inst : Add α] [inst_1 : Preorder α] [inst_2 : Preorder β] {f : β → α} [AddLeftMono α],
  Monotone f → ∀ (a : α), Monotone fun x => a + f x
Defined in
Mathlib.Algebra.Order.Monoid.Unbundled.Basic
Cited by
3 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
AddPreorderPreorderAddLeftMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

min_add_add_left · cited by 2min_add_add_leftmax_add_add_left · cited by 2max_add_add_leftAbsolutelyContinuousOnInterval.boundedVariationOn · cited by 2AbsolutelyContinuousOnInt…Preorder · cited by 7952PreorderMonotone · cited by 1397MonotoneAddLeftMono · cited by 687AddLeftMonoMonotone.comp · cited by 67Monotone.compadd_right_mono · cited by 7add_right_monoMonotone.const_addCITED BYCITES

Cites5

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

Cited by3

Results whose statement or proof uses this declaration.