Theorems · Theorem · nonassociative algebras
NonUnitalAlgebra.adjoin_empty
∀ (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], NonUnitalAlgebra.adjoin R ∅ = ⊥
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 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 · cited by 53,352
- Modulestatement and proof · cited by 20,661
- CommSemiringstatement and proof · cited by 10,911
- Bot.botstatement and proof · cited by 4,720
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- NonUnitalSubalgebrastatement · cited by 215
- GaloisConnection.l_botproof · cited by 63
- NonUnitalAlgebra.adjoinstatement and proof · cited by 33
- NonUnitalAlgebra.gcproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- NonUnitalStarAlgebra.mem_botproof · cited by 0