Theorems · Theorem · group theory

AddSubmonoid.mem_smul_pointwise_iff_exists

∀ {M : Type u_3} {A : Type u_4} [inst : Monoid M] [inst_1 : AddMonoid A] [inst_2 : DistribMulAction M A] (a : A) (m : M)
  (S : AddSubmonoid A), a ∈ m • S ↔ ∃ s ∈ S, m • s = a

Defined in: Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise
Cited by: 0 results in Mathlib
Foundations: Depth 22 from the axioms · uses propext, Quot.sound
Assumes: Monoid AddMonoid DistribMulAction

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Monoidstatement and proof · cited by 3,887
AddMonoidstatement and proof · cited by 2,864
AddSubmonoidstatement and proof · cited by 1,178
DistribMulActionstatement and proof · cited by 584
AddSubmonoid.pointwiseMulActionstatement · cited by 23
Set.mem_smul_setproof · cited by 16

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