Theorems · Theorem · ring theory
StarAlgebra.subset_adjoin
∀ (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 : Set A), s ⊆ ↑(StarAlgebra.adjoin R s)- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 8,199
- LE.le.transproof · cited by 3,151
- StarRingstatement and proof · cited by 1,686
- StarModulestatement and proof · cited by 570
- StarSubalgebrastatement · cited by 194
- Set.subset_union_leftproof · cited by 142
- Algebra.subset_adjoinproof · cited by 109
- StarAlgebra.adjoinstatement · cited by 42
Cited by10
Results whose statement or proof uses this declaration.
- StarAlgebra.adjoin_nonUnitalStarSubalgebraproof · cited by 2
- NonUnitalStarAlgebra.adjoin_le_starAlgebra_adjoinproof · cited by 2
- StarAlgebra.adjoin_inductionstatement and proof · cited by 2
- StarAlgebra.adjoin_induction_subtypestatement and proof · cited by 2
- StarAlgHom.ext_adjoinproof · cited by 1
- StarAlgebra.elemental.starAlgHomClass_extproof · cited by 1
- StarAlgebra.adjoin_eqproof · cited by 0
- StarAlgebra.mem_adjoin_of_memproof · cited by 0
- Subalgebra.starClosure_eq_adjoinproof · cited by 0
- StarAlgebra.adjoin_induction₂statement and proof · cited by 0