Theorems · Theorem · commutative algebra

Submodule.mem_set_smul_of_mem_mem

∀ {R : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {S : Type u_4}
  [inst_3 : Monoid S] [inst_4 : DistribMulAction S M] {s : Set S} {N : Submodule R M} {r : S} {m : M},
  r ∈ s → m ∈ N → r • m ∈ s • N

Defined in

Mathlib.Algebra.Module.Submodule.Pointwise

Cited by

9 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Quot.sound

Assumes

SemiringAddCommMonoidModuleMonoidDistribMulAction