no goals
ι : Sort ?u.65829
α : Type u
β : Type v
inst✝¹ : PseudoMetricSpace α
inst✝ : PseudoMetricSpace β
s t u : Set α
x y : α
Φ : α → β
h : IsClosed s
hs : Set.Nonempty s
⊢ x ∈ s ↔ infDist x s = 0
rw [← mem_closure_iff_infDist_zero hs, h.closure_eq]