Theorems · Theorem · ring theory
Algebra.adjoin_union
∀ {R : Type uR} {A : Type uA} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (s t : Set A),
Algebra.adjoin R (s ∪ t) = Algebra.adjoin R s ⊔ Algebra.adjoin R t- Cited by
- 7 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.
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
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinstatement · cited by 535
- GaloisConnection.l_supproof · cited by 81
- Algebra.gcproof · cited by 7
Cited by7
Results whose statement or proof uses this declaration.
- Algebra.EssFiniteType.compproof · cited by 7
- Subalgebra.FG.supproof · cited by 2
- Algebra.adjoin_insert_algebraMapproof · cited by 2
- IsCyclotomicExtension.lcm_supproof · cited by 1
- Subalgebra.comap_map_eqproof · cited by 1
- StarAlgebra.adjoin_eq_starClosure_adjoinproof · cited by 1
- IsDedekindDomain.adjoin_union_eq_top_of_isCoprime_differentialIdealproof · cited by 0