no goals
α : Type u_1
inst✝ : MetricSpace α
K : ℝ≥0
f : α → α
hf : ContractingWith K f
x y : α
hy : IsFixedPt f y
⊢ dist x y ≤ dist x (f x) / (1 - ↑K)
simpa only [hy.eq, dist_self, add_zero] using hf.dist_inequality x y