Theorems · Theorem · general topology
Metric.vadd_closedBall
∀ {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), c +ᵥ Metric.closedBall x r = Metric.closedBall (c +ᵥ x) r- Cited by
- 7 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- AddGroupstatement and proof · cited by 4,410
- HVAdd.hVAddstatement · cited by 1,820
- PseudoMetricSpacestatement and proof · cited by 1,550
- AddActionstatement and proof · cited by 820
- Metric.closedBallstatement · cited by 704
- Set.vaddSetstatement · cited by 403
- IsIsometricVAddstatement and proof · cited by 74
- IsometryEquiv.constVAddproof · cited by 8
- IsometryEquiv.image_closedBallproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- singleton_add_closedBallproof · cited by 4
- vadd_closedBall_zeroproof · cited by 4
- Metric.preimage_vadd_closedBallproof · cited by 2
- Valued.integer.totallyBounded_iff_finite_residueFieldproof · cited by 1
- closedBall_add_closedBallproof · cited by 1
- FiniteDimensional.of_isCompact_closedBallproof · cited by 1
- Seminorm.vadd_closedBallproof · cited by 0