Theorems · Theorem · functional analysis
Seminorm.restrictScalars_closedBall
∀ (𝕜 : Type u_3) {E : Type u_7} {𝕜' : Type u_12} [inst : NormedField 𝕜] [inst_1 : SeminormedRing 𝕜']
[inst_2 : SMul 𝕜 𝕜'] [inst_3 : NormSMulClass 𝕜 𝕜'] [inst_4 : NormOneClass 𝕜'] [inst_5 : AddCommGroup E]
[inst_6 : Module 𝕜' E] [inst_7 : SMul 𝕜 E] [inst_8 : IsScalarTower 𝕜 𝕜' E] (p : Seminorm 𝕜' E),
(Seminorm.restrictScalars 𝕜 p).closedBall = p.closedBall- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- IsScalarTowerstatement and proof · cited by 3,896
- NormedFieldstatement and proof · cited by 1,084
- SeminormedRingstatement and proof · cited by 446
- Seminormstatement and proof · cited by 272
- NormOneClassstatement and proof · cited by 136
- NormSMulClassstatement and proof · cited by 107
- Seminorm.closedBallstatement · cited by 45
- Seminorm.restrictScalarsstatement · cited by 4
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