Theorems · Theorem · ring theory
Algebra.adjoin_eq_of_le
∀ {R : Type uR} {A : Type uA} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] {s : Set A}
(S : Subalgebra R A), s ⊆ ↑S → S ≤ Algebra.adjoin R s → Algebra.adjoin R s = S- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 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.
Cites9
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
- SetLike.coestatement and proof · cited by 8,199
- le_antisymmproof · cited by 2,068
- Subalgebrastatement and proof · cited by 1,353
- Algebra.adjoinstatement and proof · cited by 535
- Algebra.adjoin_leproof · cited by 36
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.adjoin_eqproof · cited by 3