Theorems · Theorem · group theory

Submonoid.smul_mem_pointwise_smul_iff

∀ {α : Type u_1} {M : Type u_3} [inst : Monoid M] [inst_1 : Group α] [inst_2 : MulDistribMulAction α M] {a : α}
  {S : Submonoid M} {x : M}, a • x ∈ a • S ↔ x ∈ S

Defined in: Mathlib.Algebra.Group.Submonoid.Pointwise
Cited by: 0 results in Mathlib
Foundations: Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Monoid Group MulDistribMulAction

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Groupstatement and proof · cited by 6,238
Monoidstatement and proof · cited by 3,887
Submonoidstatement and proof · cited by 3,086
MulDistribMulActionstatement and proof · cited by 120
Submonoid.pointwiseMulActionstatement · cited by 20
Set.smul_mem_smul_set_iffproof · cited by 14

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