Singleton images under an injective function #
Mirror of Mathlib/Data/Set/Image.lean: the image of a set under an injective function is a
singleton iff the set is, the singleton rung beside Function.Injective.subsingleton_image_iff.
[UPSTREAM]
theorem
Function.Injective.exists_image_eq_singleton_iff
{α : Type u_1}
{β : Type u_2}
{f : α → β}
(hf : Injective f)
{s : Set α}
:
(∃ (b : β), f '' s = {b}) ↔ ∃ (a : α), s = {a}
The image of a set under an injective function is a singleton iff the set is. [UPSTREAM]