Theorems · Theorem · functional analysis
Seminorm.coe_sSup_eq
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
{s : Set (Seminorm 𝕜 E)}, BddAbove s → ⇑(sSup s) = ⨆ p, ⇑↑p- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Set.Elemstatement · cited by 7,166
- iSupstatement · cited by 2,415
- NormedFieldstatement and proof · cited by 1,084
- SupSet.sSupstatement · cited by 954
- BddAbovestatement and proof · cited by 620
- Seminormstatement and proof · cited by 272
- Seminorm.coe_sSup_eq'proof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Seminorm.coe_iSup_eqproof · cited by 3
- Seminorm.sSup_applyproof · cited by 2