Theorems · Theorem · ring theory
Algebra.sInf_toSubsemiring
∀ {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).toSubsemiring = sInf (Subalgebra.toSubsemiring '' S)- Cited by
- 2 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.
Cites17
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.coeproof · cited by 8,199
- Set.imagestatement and proof · cited by 5,609
- Subalgebrastatement and proof · cited by 1,353
- Set.iInterproof · cited by 1,084
- InfSet.sInfstatement and proof · cited by 935
- Subsemiringstatement and proof · cited by 456
- SetLike.coe_injectiveproof · cited by 374
- Set.iInter_congr_Propproof · cited by 170
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.sInf_toSubfieldproof · cited by 1
- Algebra.iInf_toSubsemiringproof · cited by 0