Minimal elements of well-founded images #
Set.IsWF.exists_minimalFor, the well-founded companion of mathlib's
Set.IsPWO.exists_minimalFor: if the image of a nonempty set under f is well-founded, some
element of the set is minimal for f.
theorem
Set.IsWF.exists_minimalFor
{ι : Type u_1}
{β : Type u_2}
[Preorder β]
(f : ι → β)
(s : Set ι)
(h : (f '' s).IsWF)
(hs : s.Nonempty)
:
∃ (i : ι), MinimalFor (fun (x : ι) => x ∈ s) f i