Theorems · Theorem · general topology

Metric.preimage_vadd_ball

∀ {G : Type v} {X : Type w} [inst : PseudoMetricSpace X] [inst_1 : AddGroup G] [inst_2 : AddAction G X]
  [IsIsometricVAdd G X] (c : G) (x : X) (r : ℝ), (fun x => c +ᵥ x) ⁻¹' Metric.ball x r = Metric.ball (-c +ᵥ x) r

Defined in

Mathlib.Topology.MetricSpace.IsometricSMul

Cited by

2 results in Mathlib

Foundations

Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpaceAddGroupAddActionIsIsometricVAdd