Theorems · Theorem · ring theory
NonUnitalStarAlgebra.coe_iInf
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : NonUnitalSemiring A]
[inst_3 : StarRing A] [inst_4 : Module R A] [inst_5 : IsScalarTower R A A] [inst_6 : SMulCommClass R A A]
[inst_7 : StarModule R A] {ι : Sort u_1} {S : ι → NonUnitalStarSubalgebra R A}, ↑(⨅ i, S i) = ⋂ i, ↑(S i)- Defined in
- Mathlib.Algebra.Star.NonUnitalSubalgebra
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- SetLike.coestatement and proof · cited by 8,199
- Set.rangeproof · cited by 4,705
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- iInfstatement · cited by 1,690
- StarRingstatement and proof · cited by 1,686
- Set.iInterstatement and proof · cited by 1,084
- StarModulestatement and proof · cited by 570
- NonUnitalSemiringstatement and proof · cited by 339
Cited by2
Results whose statement or proof uses this declaration.
- NonUnitalStarAlgebra.map_iInfproof · cited by 0
- NonUnitalStarAlgebra.iInf_toNonUnitalSubalgebraproof · cited by 0