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Theorems · Theorem · order theory

Set.IsPWO.image_of_monotone

∀ {α : Type u_2} {β : Type u_3} [inst : Preorder α] [inst_1 : Preorder β] {s : Set α},
  s.IsPWO → ∀ {f : α → β}, Monotone f → (f '' s).IsPWO
Defined in
Mathlib.Order.WellFoundedSet
Cited by
5 results in Mathlib
Foundations
Depth 10 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderPreorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.IsPWO.vadd · cited by 3IsPWO.vaddSet.IsPWO.add · cited by 2IsPWO.addSet.IsPWO.mul · cited by 2IsPWO.mulSet.IsPWO.smul · cited by 2IsPWO.smulSet.PartiallyWellOrderedOn.imageProdLex · cited by 1PartiallyWellOrderedOn.im…Set · cited by 53352SetPreorder · cited by 7952PreorderSet.image · cited by 5609Set.imageMonotone · cited by 1397MonotoneSet.IsPWO · cited by 99Set.IsPWOMonotone.monotoneOn · cited by 43Monotone.monotoneOnSet.PartiallyWellOrderedOn.image_of_monotone_on · cited by 4PartiallyWellOrderedOn.im…IsPWO.image_of_monotoneCITED BYCITES

Cites7

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

Cited by5

Results whose statement or proof uses this declaration.