Theorems · Theorem · functional analysis
Seminorm.sSup_empty
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E], sSup ∅ = ⊥- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Realproof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Set.Elemproof · cited by 7,166
- Bot.botstatement and proof · cited by 4,720
- NormedFieldstatement and proof · cited by 1,084
- SupSet.sSupstatement · cited by 954
- Seminormstatement · cited by 272
- Seminorm.extproof · cited by 17
- Real.iSup_of_isEmptyproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- Seminorm.closedBall_iSupproof · cited by 1