Theorems · Theorem · functional analysis
SeminormFamily.basisSets_intersect
∀ {R : Type u_1} {E : Type u_6} {ι : Type u_9} [inst : SeminormedRing R] [inst_1 : AddCommGroup E] [inst_2 : Module R E]
(p : SeminormFamily R E ι) (U V : Set E), U ∈ p.basisSets → V ∈ p.basisSets → ∃ z ∈ p.basisSets, z ⊆ U ∩ V- Cited by
- 0 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- Realproof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- Finsetproof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- Set.iInterproof · cited by 1,084
- Finset.supproof · cited by 530
- SeminormedRingstatement and proof · cited by 446
- min_le_leftproof · cited by 105
- min_le_rightproof · cited by 88
- Seminorm.ballproof · cited by 78
- Set.subset_interproof · cited by 74
Cited by1
Results whose statement or proof uses this declaration.
- SeminormFamily.addGroupFilterBasisproof · cited by 3