Theorems · Theorem · ring theory
Subalgebra.toSubsemiring_subtype
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (S : Subalgebra R A),
S.subtype = ↑S.val- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- AlgHomstatement · cited by 3,236
- Subalgebrastatement and proof · cited by 1,353
- RingHomClass.toRingHomstatement · cited by 746
- Subsemiringstatement · cited by 456
- Subalgebra.toSubsemiringstatement · cited by 115
- Subalgebra.valstatement · cited by 104
- Subsemiring.subtypestatement · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Subalgebra.rangeS_algebraMapproof · cited by 1