Theorems · Theorem · ring theory
Algebra.coe_iInf
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] {ι : Sort u_1}
{S : ι → Subalgebra R A}, ↑(⨅ i, S i) = ⋂ i, ↑(S i)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Subalgebrastatement and proof · cited by 1,353
- Set.iInterstatement and proof · cited by 1,084
- Set.iInter_congr_Propproof · cited by 170
- Set.iInter_existsproof · cited by 44
- Set.iInter_iInter_eq'proof · cited by 22
Cited by3
Results whose statement or proof uses this declaration.
- StarSubalgebra.iInf_toSubalgebraproof · cited by 0
- Algebra.iInf_toSubmoduleproof · cited by 0
- Algebra.map_iInfproof · cited by 0