Mathlib Map

Theorems · Theorem · order theory

Set.infinite_image_iff

∀ {α : Type u} {β : Type v} {s : Set α} {f : α → β}, Set.InjOn f s → ((f '' s).Infinite ↔ s.Infinite)
Defined in
Mathlib.Data.Set.Finite.Basic
Cited by
7 results in Mathlib
Foundations
Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.infinite_range_of_injective · cited by 9Set.infinite_range_of_inj…Set.Infinite.image · cited by 6Infinite.imagefinsum_mem_image' · cited by 2finsum_mem_image'finprod_mem_image' · cited by 2finprod_mem_image'Set.infinite_of_injOn_mapsTo · cited by 1Set.infinite_of_injOn_map…Set.infinite_smul_set · cited by 1Set.infinite_smul_setSet.infinite_vadd_set · cited by 1Set.infinite_vadd_setSet · cited by 53352SetSet.image · cited by 5609Set.imageSet.InjOn · cited by 543Set.InjOnSet.Infinite · cited by 263Set.InfiniteSet.finite_image_iff · cited by 16Set.finite_image_iffSet.infinite_image_iffCITED BYCITES

Cites5

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

Cited by7

Results whose statement or proof uses this declaration.