Theorems · Theorem · functional analysis
Bornology.IsVonNBounded.of_add_left
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] [ContinuousSMul 𝕜 E] [ContinuousAdd E] {s t : Set E},
Bornology.IsVonNBounded 𝕜 (s + t) → t.Nonempty → Bornology.IsVonNBounded 𝕜 s- Defined in
- Mathlib.Analysis.LocallyConvex.Bounded
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Set.Nonemptystatement and proof · cited by 2,627
- add_commproof · cited by 1,535
- NormedFieldstatement and proof · cited by 1,084
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousAddstatement and proof · cited by 777
- Set.addstatement · cited by 338
- Bornology.IsVonNBoundedstatement and proof · cited by 136
- Bornology.IsVonNBounded.of_add_rightproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Bornology.isVonNBounded_add_of_nonemptyproof · cited by 1
- Bornology.IsVonNBounded.of_sub_leftproof · cited by 0