Theorems · Theorem · nonassociative algebras
NonUnitalAlgebra.subset_adjoin
∀ (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 : Set A}, s ⊆ ↑(NonUnitalAlgebra.adjoin R s)- Cited by
- 13 results in Mathlib
- Foundations
- Depth 67 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
- Modulestatement and proof · cited by 20,661
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement · cited by 8,199
- IsScalarTowerstatement and proof · cited by 3,896
- LE.le.transproof · cited by 3,151
- SMulCommClassstatement and proof · cited by 1,927
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Submodule.subset_spanproof · cited by 234
- NonUnitalSubalgebrastatement · cited by 215
- NonUnitalAlgebra.adjoinstatement · cited by 33
- NonUnitalSubsemiring.subset_closureproof · cited by 10
Cited by13
Results whose statement or proof uses this declaration.
- NonUnitalStarAlgebra.subset_adjoinproof · cited by 5
- NonUnitalAlgebra.adjoin_inductionstatement and proof · cited by 4
- NonUnitalStarAlgebra.self_mem_adjoin_singletonproof · cited by 2
- NonUnitalAlgebra.adjoin_eq_spanproof · cited by 2
- NonUnitalAlgebra.self_mem_adjoin_singletonproof · cited by 1
- NonUnitalStarAlgebra.adjoin_inductionproof · cited by 1
- NonUnitalSubalgebra.star_adjoin_commproof · cited by 1
- NonUnitalAlgebra.adjoin_eqproof · cited by 1
- NonUnitalAlgebra.adjoin_induction₂statement and proof · cited by 0
- NonUnitalAlgebra.mem_adjoin_of_memproof · cited by 0
- NonUnitalStarAlgebra.star_subset_adjoinproof · cited by 0
- Algebra.adjoin_nonUnitalSubalgebraproof · cited by 0