Theorems · Theorem · ring theory
Subalgebra.toSubring_subtype
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] (S : Subalgebra R A),
S.toSubring.subtype = ↑S.val- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Quot.sound
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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- AlgHomstatement · cited by 3,236
- Subalgebrastatement and proof · cited by 1,353
- RingHomClass.toRingHomstatement · cited by 746
- Subringstatement · cited by 602
- Subalgebra.valstatement · cited by 104
- Subalgebra.toSubringstatement · cited by 30
- Subring.subtypestatement · cited by 22
Cited by2
Results whose statement or proof uses this declaration.
- IsAlgebraic.restrictScalarsproof · cited by 6
- Subalgebra.range_algebraMapproof · cited by 3