Theorems · Theorem · ring theory
Algebra.coe_sInf
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
(S : Set (Subalgebra R A)), ↑(sInf S) = ⋂ s ∈ S, ↑s- Cited by
- 7 results in Mathlib
- Foundations
- Depth 75 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.
Cites9
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
- Subalgebrastatement and proof · cited by 1,353
- Set.iInterstatement · cited by 1,084
- InfSet.sInfstatement · cited by 935
- sInf_imageproof · cited by 25
Cited by7
Results whose statement or proof uses this declaration.
- Algebra.coe_iInfproof · cited by 3
- Algebra.sInf_toSubsemiringproof · cited by 2
- IntermediateField.sInf_toSubalgebraproof · cited by 2
- Algebra.mem_sInfproof · cited by 0
- Algebra.sInf_toSubmoduleproof · cited by 0
- StarSubalgebra.sInf_toSubalgebraproof · cited by 0
- IntermediateField.iInf_toSubalgebraproof · cited by 0