Theorems · Theorem · ring theory
StarSubalgebra.coe_sInf
∀ {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] (S : Set (StarSubalgebra R A)),
↑(sInf S) = ⋂ s ∈ S, ↑s- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 81 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
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement · cited by 8,199
- StarRingstatement and proof · cited by 1,686
- Set.iInterstatement · cited by 1,084
- InfSet.sInfstatement · cited by 935
- StarModulestatement and proof · cited by 570
- StarSubalgebrastatement and proof · cited by 194
- sInf_imageproof · cited by 25
Cited by3
Results whose statement or proof uses this declaration.
- StarSubalgebra.coe_iInfproof · cited by 2
- StarSubalgebra.mem_sInfproof · cited by 0
- StarSubalgebra.sInf_toSubalgebraproof · cited by 0