Theorems · Theorem · ring theory
StarSubalgebra.coe_iInf
∀ {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : Semiring A]
[inst_3 : Algebra R A] [inst_4 : StarRing A] [inst_5 : StarModule R A] {ι : Sort u_5} {S : ι → StarSubalgebra R A},
↑(⨅ i, S i) = ⋂ i, ↑(S i)- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- Set.rangeproof · cited by 4,705
- 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
- StarSubalgebrastatement and proof · cited by 194
- Set.iInter_congr_Propproof · cited by 170
Cited by2
Results whose statement or proof uses this declaration.
- StarSubalgebra.iInf_toSubalgebraproof · cited by 0
- StarSubalgebra.map_iInfproof · cited by 0