Theorems · Theorem · group theory

Set.smul_set_eq_univ

∀ {α : Type u_2} {β : Type u_3} [inst : Group α] [inst_1 : MulAction α β] {s : Set β} {a : α},
  a • s = Set.univ ↔ s = Set.univ

Defined in: Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 26 from the axioms · uses propext, Quot.sound
Assumes: Group MulAction

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
Groupstatement and proof · cited by 6,238
Set.univstatement and proof · cited by 3,945
MulActionstatement and proof · cited by 1,294
Set.smulSetstatement · cited by 608
Set.smul_set_univproof · cited by 10
smul_eq_iff_eq_inv_smulproof · cited by 9

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.