Mathlib Map

Theorems · Theorem · commutative algebra

dvd_smul_of_dvd

∀ {R : Type u_1} {M : Type u_2} [inst : SMul M R] [inst_1 : Semigroup R] [SMulCommClass M R R] {x y : R} (m : M),
  x ∣ y → x ∣ m • y
Defined in
Mathlib.Algebra.Ring.Divisibility.Lemmas
Cited by
2 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
SMulSemigroupSMulCommClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

dvd_nsmul_of_dvd · cited by 1dvd_nsmul_of_dvddvd_zsmul_of_dvd · cited by 0dvd_zsmul_of_dvdSMulCommClass · cited by 1927SMulCommClassSemigroup · cited by 202Semigroupmul_smul_comm · cited by 65mul_smul_commdvd_smul_of_dvdCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.