Theorems · Theorem · general topology
Absorbs.add
∀ {M : Type u_1} {E : Type u_2} [inst : Bornology M] {s₁ s₂ t₁ t₂ : Set E} [inst_1 : AddZeroClass E]
[inst_2 : DistribSMul M E], Absorbs M s₁ t₁ → Absorbs M s₂ t₂ → Absorbs M (s₁ + s₂) (t₁ + t₂)- Defined in
- Mathlib.Topology.Bornology.Absorbs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- AddZeroClassstatement and proof · cited by 1,237
- Filter.Eventually.monoproof · cited by 646
- Set.addstatement · cited by 338
- smul_addproof · cited by 263
- Bornologystatement and proof · cited by 188
- DistribSMulstatement and proof · cited by 117
- Filter.Eventually.mpproof · cited by 78
- Absorbsstatement and proof · cited by 59
- Set.add_subset_addproof · cited by 18
- Absorbs.eventuallyproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Bornology.IsVonNBounded.addproof · cited by 3
- Absorbent.vadd_absorbsproof · cited by 1
- Absorbs.subproof · cited by 0