Theorems · Theorem · nonassociative algebras
NonUnitalAlgebra.eq_top_iff
∀ {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 = ⊤ ↔ ∀ (x : A), x ∈ S- Cited by
- 2 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement and proof · cited by 9,680
- 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
- NonUnitalSubalgebra.extproof · cited by 8
- NonUnitalAlgebra.mem_topproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- NonUnitalAlgebra.range_eq_topproof · cited by 0
- NonUnitalAlgebra.comap_topproof · cited by 0