Theorems · Theorem · ring theory
NonUnitalStarAlgebra.adjoin_le
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : NonUnitalSemiring A]
[inst_3 : StarRing A] [inst_4 : Module R A] [inst_5 : IsScalarTower R A A] [inst_6 : SMulCommClass R A A]
[inst_7 : StarModule R A] {S : NonUnitalStarSubalgebra R A} {s : Set A}, s ⊆ ↑S → NonUnitalStarAlgebra.adjoin R s ≤ S- Defined in
- Mathlib.Algebra.Star.NonUnitalSubalgebra
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Modulestatement and proof · cited by 20,661
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- StarModulestatement and proof · cited by 570
- NonUnitalSemiringstatement and proof · cited by 339
- NonUnitalStarSubalgebrastatement and proof · cited by 196
- NonUnitalStarAlgebra.adjoinstatement · cited by 43
- GaloisConnection.l_leproof · cited by 28
Cited by5
Results whose statement or proof uses this declaration.
- NonUnitalStarAlgebra.adjoin_le_starAlgebra_adjoinproof · cited by 2
- NonUnitalStarAlgebra.adjoin_eqproof · cited by 1
- NonUnitalStarAlgebra.elemental.le_of_memproof · cited by 1
- cfcₙAux_mem_range_inrproof · cited by 1
- NonUnitalSubalgebra.starClosure_eq_adjoinproof · cited by 0