Theorems · Theorem · ring theory
Algebra.adjoin_iUnion
∀ {R : Type uR} {A : Type uA} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] {α : Type u_2}
(s : α → Set A), Algebra.adjoin R (Set.iUnion s) = ⨆ i, Algebra.adjoin R (s i)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Set.iUnionstatement · cited by 2,483
- iSupstatement · cited by 2,415
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinstatement · cited by 535
- GaloisConnection.l_iSupproof · cited by 78
- Algebra.gcproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.adjoin_attach_biUnionproof · cited by 1