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Theorems · Theorem · general topology

EMetric.preimage_add_right_closedBall

Deprecated since 2026-01-24Use Metric.preimage_add_right_closedEBall instead.

∀ {G : Type v} [inst : AddGroup G] [inst_1 : PseudoEMetricSpace G] [IsIsometricVAdd Gᵃᵒᵖ G] (a b : G) (r : ENNReal),
  (fun x => x + a) ⁻¹' Metric.closedEBall b r = Metric.closedEBall (b - a) r

Alias of Metric.preimage_add_right_closedEBall.

Defined in
Mathlib.Topology.MetricSpace.IsometricSMul
Cited by
0 results in Mathlib
Foundations
Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupPseudoEMetricSpaceIsIsometricVAdd
Mathlib docsSourceLoogleLeanSearch

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Set · cited by 53352SetENNReal · cited by 9879ENNRealSet.preimage · cited by 4946Set.preimageAddGroup · cited by 4410AddGroupPseudoEMetricSpace · cited by 1536PseudoEMetricSpaceAddOpposite · cited by 452AddOppositeMetric.closedEBall · cited by 107Metric.closedEBallIsIsometricVAdd · cited by 74IsIsometricVAddMetric.preimage_add_right_closedEBall · cited by 1Metric.preimage_add_right…EMetric.preimage_add_right_cl…CITED BYCITES

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