Theorems · Theorem · functional analysis
Seminorm.ball_zero_absorbs_ball_zero
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
(p : Seminorm 𝕜 E) {r₁ r₂ : ℝ}, 0 < r₁ → Absorbs 𝕜 (p.ball 0 r₁) (p.ball 0 r₂)- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- AddCommGroupstatement and proof · cited by 12,871
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- NormedDivisionRingstatement and proof · cited by 360
- mul_le_mul_of_nonneg_rightproof · cited by 301
- Seminormstatement and proof · cited by 272
- norm_pos_iffproof · cited by 168
Cited by3
Results whose statement or proof uses this declaration.
- Seminorm.absorbent_ball_zeroproof · cited by 4
- NormedSpace.isVonNBounded_of_isBoundedproof · cited by 4
- WithSeminorms.isVonNBounded_iff_finset_seminorm_boundedproof · cited by 2