Theorems · Theorem · ring theory
Algebra.sSup_toSubsemiring
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
(S : Set (Subalgebra R A)), S.Nonempty → (sSup S).toSubsemiring = sSup (Subalgebra.toSubsemiring '' S)- Cited by
- 1 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.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- Algebra.algebraMapproof · cited by 4,706
- Set.rangeproof · cited by 4,705
- Set.Nonemptystatement and proof · cited by 2,627
- Subalgebrastatement and proof · cited by 1,353
- SupSet.sSupstatement and proof · cited by 954
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.iSup_toSubsemiringproof · cited by 0