Theorems · Theorem · functional analysis
Seminorm.ball_smul
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : SMul 𝕜 E]
(p : Seminorm 𝕜 E) {c : NNReal}, 0 < c → ∀ (r : ℝ) (x : E), (c • p).ball x r = p.ball x (r / ↑c)- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- AddCommGroupstatement and proof · cited by 12,871
- NNRealstatement and proof · cited by 4,310
- Set.extproof · cited by 2,266
- mul_commproof · cited by 2,262
- NNReal.toRealstatement and proof · cited by 1,260
- SeminormedRingstatement and proof · cited by 446
- smul_eq_mulproof · cited by 357
- Seminormstatement and proof · cited by 272
- smul_applyproof · cited by 229
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