Theorems · Theorem · ring theory
StarAlgebra.adjoin_le_iff
∀ {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},
StarAlgebra.adjoin R s ≤ S ↔ s ⊆ ↑S- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 1 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.
Cites10
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
- StarRingstatement and proof · cited by 1,686
- StarModulestatement and proof · cited by 570
- StarSubalgebrastatement and proof · cited by 194
- StarAlgebra.adjoinstatement · cited by 42
- StarAlgebra.gcproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Unitization.starLift_rangeproof · cited by 1