Theorems · Theorem · nonassociative algebras
NonUnitalAlgebra.coe_sInf
∀ {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 (NonUnitalSubalgebra R A)),
↑(sInf S) = ⋂ s ∈ S, ↑s- Cited by
- 5 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 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
- SMulCommClassstatement and proof · cited by 1,927
- Set.iInterstatement · cited by 1,084
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- InfSet.sInfstatement · cited by 935
- NonUnitalSubalgebrastatement and proof · cited by 215
- sInf_imageproof · cited by 25
Cited by5
Results whose statement or proof uses this declaration.
- NonUnitalAlgebra.coe_iInfproof · cited by 3
- NonUnitalStarAlgebra.sInf_toNonUnitalSubalgebraproof · cited by 0
- NonUnitalAlgebra.mem_sInfproof · cited by 0
- NonUnitalAlgebra.sInf_toNonUnitalSubsemiringproof · cited by 0
- NonUnitalAlgebra.sInf_toSubmoduleproof · cited by 0