Theorems · Theorem · commutative algebra

Submodule.set_smul_eq_iSup

∀ {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] [inst_5 : SMulCommClass S R M] (s : Set S) (N : Submodule R M),
  s • N = ⨆ a ∈ s, a • N

Defined in

Mathlib.Algebra.Module.Submodule.Pointwise

Cited by

2 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleMonoidDistribMulActionSMulCommClass