Theorems · Theorem · commutative algebra

Submodule.set_smul_le_iff

∀ {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 p : Submodule R M),
  s • N ≤ p ↔ ∀ ⦃r : S⦄ ⦃n : M⦄, r ∈ s → n ∈ N → r • n ∈ p

Defined in

Mathlib.Algebra.Module.Submodule.Pointwise

Cited by

0 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleMonoidDistribMulAction