Theorems · Theorem · ring theory
Subalgebra.smul_mem_pointwise_smul
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] {R' : Type u_3}
[inst_3 : Semiring R'] [inst_4 : MulSemiringAction R' A] [inst_5 : SMulCommClass R' R A] (m : R') (r : A)
(S : Subalgebra R A), r ∈ S → m • r ∈ m • S- Cited by
- 0 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
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Cites8
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
- SMulCommClassstatement and proof · cited by 1,927
- Subalgebrastatement and proof · cited by 1,353
- MulSemiringActionstatement and proof · cited by 423
- Set.smul_mem_smul_setproof · cited by 39
- Subalgebra.pointwiseMulActionstatement · cited by 5
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