Theorems · Theorem · group theory

Set.smul_univ

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

Defined in: Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 24 from the axioms · uses propext, Quot.sound
Assumes: Group MulAction

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Cites8

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
Set.Nonemptystatement and proof · cited by 2,627
MulActionstatement and proof · cited by 1,294
Set.smulstatement · cited by 110
Set.eq_univ_of_forallproof · cited by 80
smul_inv_smulproof · cited by 53

Cited by1

Results whose statement or proof uses this declaration.

Finset.smul_univproof · cited by 0