Theorems · Theorem · group theory

Set.iUnion_vadd_eq_ofPred_exists

∀ {α : Type u_2} {β : Type u_3} [inst : AddGroup α] [inst_1 : AddAction α β] {s : Set β},
  ⋃ g, g +ᵥ s = {a | ∃ g, g +ᵥ a ∈ s}

Defined in: Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 16 from the axioms · uses propext, Quot.sound
Assumes: AddGroup AddAction

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Cites10

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
Set.ofPredstatement and proof · cited by 6,101
AddGroupstatement and proof · cited by 4,410
Set.iUnionstatement and proof · cited by 2,483
HVAdd.hVAddstatement and proof · cited by 1,820
AddActionstatement and proof · cited by 820
Set.vaddSetstatement · cited by 403
Set.preimage_vaddproof · cited by 14
Set.iUnion_ofPredproof · cited by 3
Set.iUnion_neg_vaddproof · cited by 1

Cited by2

Results whose statement or proof uses this declaration.

MeasureTheory.IsAddFundamentalDomain.mk_of_measure_univ_leproof · cited by 1
Set.iUnion_vadd_eq_setOf_existsproof · cited by 0