Theorems · Theorem · ring theory
Algebra.sup_toSubsemiring
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (S T : Subalgebra R A),
(S ⊔ T).toSubsemiring = S.toSubsemiring ⊔ T.toSubsemiring- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · 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
- Algebra.algebraMapproof · cited by 4,706
- Set.rangeproof · cited by 4,705
- Subalgebrastatement and proof · cited by 1,353
- NonAssocSemiringproof · cited by 805
- Subsemiringstatement and proof · cited by 456
- Subalgebra.toSubsemiringstatement and proof · cited by 115
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