Theorems · Theorem · functional analysis
Seminorm.ball_add_ball_subset
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : SMul 𝕜 E]
(p : Seminorm 𝕜 E) (r₁ r₂ : ℝ) (x₁ x₂ : E), p.ball x₁ r₁ + p.ball x₂ r₂ ⊆ p.ball (x₁ + x₂) (r₁ + r₂)- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 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.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- AddCommGroupstatement and proof · cited by 12,871
- LE.le.trans_ltproof · cited by 795
- SeminormedRingstatement and proof · cited by 446
- Set.addstatement · cited by 338
- Seminormstatement and proof · cited by 272
- Seminorm.ballstatement and proof · cited by 78
- add_lt_addproof · cited by 35
- add_sub_add_commproof · cited by 28
- SubadditiveHomClass.map_add_le_addproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- SeminormFamily.basisSets_addproof · cited by 0