Theorems · Theorem · logic and foundations
IsProperSemilinearSet.biUnion
∀ {M : Type u_1} {ι : Type u_3} [inst : AddCommMonoid M] {s : Set ι} {t : ι → Set M},
s.Finite → (∀ i ∈ s, IsProperSemilinearSet (t i)) → IsProperSemilinearSet (⋃ i ∈ s, t i)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddCommMonoidstatement and proof · cited by 12,281
- Set.iUnionstatement · cited by 2,483
- Set.Finitestatement and proof · cited by 1,814
- Set.Finite.imageproof · cited by 96
- Set.sUnion_imageproof · cited by 28
- IsProperSemilinearSetstatement and proof · cited by 10
- IsProperSemilinearSet.sUnionproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsProperSemilinearSet.biUnion_finsetproof · cited by 1
- IsSemilinearSet.isProperSemilinearSetproof · cited by 1