Theorems · Theorem · ring theory
StarAlgebra.adjoin_le
∀ {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : Semiring A]
[inst_3 : Algebra R A] [inst_4 : StarRing A] [inst_5 : StarModule R A] {S : StarSubalgebra R A} {s : Set A},
s ⊆ ↑S → StarAlgebra.adjoin R s ≤ S- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- StarRingstatement and proof · cited by 1,686
- StarModulestatement and proof · cited by 570
- StarSubalgebrastatement and proof · cited by 194
- StarAlgebra.adjoinstatement · cited by 42
- GaloisConnection.l_leproof · cited by 28
- StarAlgebra.gcproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- StarAlgebra.adjoin_nonUnitalStarSubalgebraproof · cited by 2
- StarAlgHom.adjoin_le_equalizerproof · cited by 2
- StarAlgebra.elemental.le_of_memproof · cited by 1
- Subalgebra.starClosure_eq_adjoinproof · cited by 0
- StarAlgebra.adjoin_eqproof · cited by 0