Theorems · Theorem · functional analysis
Metric.star_ball
∀ {E : Type u_2} [inst : SeminormedAddCommGroup E] [inst_1 : StarAddMonoid E] [NormedStarGroup E] (x : E) (r : ℝ),
star (Metric.ball x r) = Metric.ball (star x) r- Defined in
- Mathlib.Analysis.CStarAlgebra.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Set.preimageproof · cited by 4,946
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Star.starstatement and proof · cited by 1,082
- Metric.ballstatement and proof · cited by 735
- StarAddMonoidstatement and proof · cited by 296
- star_starproof · cited by 135
- NormedStarGroupstatement and proof · cited by 54
- star_isometryproof · cited by 6
- Isometry.preimage_ballproof · cited by 4
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