Theorems · Theorem · nonassociative algebras
NonUnitalAlgebra.adjoin_le
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : NonUnitalNonAssocSemiring A] [inst_2 : Module R A]
[inst_3 : IsScalarTower R A A] [inst_4 : SMulCommClass R A A] {S : NonUnitalSubalgebra R A} {s : Set A},
s ⊆ ↑S → NonUnitalAlgebra.adjoin R s ≤ S- Cited by
- 6 results in Mathlib
- Foundations
- Depth 69 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
- 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
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- NonUnitalSubalgebrastatement and proof · cited by 215
- NonUnitalAlgebra.adjoinstatement · cited by 33
- GaloisConnection.l_leproof · cited by 28
- NonUnitalAlgebra.gcproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- NonUnitalAlgebra.adjoin_le_centralizer_centralizerproof · cited by 4
- NonUnitalAlgebra.adjoin_inductionproof · cited by 4
- NonUnitalAlgebra.adjoin_le_algebra_adjoinproof · cited by 1
- NonUnitalSubalgebra.star_adjoin_commproof · cited by 1
- NonUnitalAlgebra.adjoin_eqproof · cited by 1
- NonUnitalAlgebra.elemental.le_of_memproof · cited by 1