Theorems · Theorem · ring theory
Subalgebra.sub_mem
∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] (S : Subalgebra R A) {x y : A},
x ∈ S → y ∈ S → x - y ∈ S- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Ringstatement and proof · cited by 7,463
- Subalgebrastatement and proof · cited by 1,353
- sub_memproof · cited by 40
Cited by8
Results whose statement or proof uses this declaration.
- Subalgebra.SeparatesPoints.rclike_to_realproof · cited by 2
- IsPrimitiveRoot.subOneIntegralPowerBasisOfPrimePow_genstatement and proof · cited by 1
- MvPolynomial.esymmAlgHom_fin_bijectiveproof · cited by 1
- ContinuousMap.inf_mem_subalgebra_closureproof · cited by 1
- IsPrimitiveRoot.self_sub_one_pow_dvd_orderproof · cited by 1
- IsPrimitiveRoot.subOneIntegralPowerBasis_genstatement and proof · cited by 0
- MvPolynomial.IsSymmetric.subproof · cited by 0