Theorems · Theorem · nonassociative algebras
NonUnitalAlgebra.adjoin.congr_simp
∀ (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 s_1 : Set A),
s = s_1 → NonUnitalAlgebra.adjoin R s = NonUnitalAlgebra.adjoin R s_1- Cited by
- 2 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.
Cites8
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
- 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
- NonUnitalAlgebra.adjoinstatement and proof · cited by 33
Cited by2
Results whose statement or proof uses this declaration.
- NonUnitalSubalgebra.star_adjoin_commproof · cited by 1
- NonUnitalAlgHom.map_adjoin_singletonproof · cited by 0