Theorems · Theorem · group theory

Set.iUnion_inv_smul

∀ {α : Type u_2} {β : Type u_3} [inst : Group α] [inst_1 : MulAction α β] {s : Set β}, ⋃ g, g⁻¹ • s = ⋃ g, g • s

Defined in: Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 12 from the axioms · uses propext, Quot.sound
Assumes: Group MulAction

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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.iUnionstatement · cited by 2,483
MulActionstatement and proof · cited by 1,294
Set.smulSetstatement · cited by 608
Function.Surjective.iSup_congrproof · cited by 14
inv_surjectiveproof · cited by 6

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.IsFundamentalDomain.fundamentalInteriorproof · cited by 0