Theorems · Theorem · group theory

Set.mem_neg_vadd_set_iff

∀ {α : Type u_2} {β : Type u_3} [inst : AddGroup α] [inst_1 : AddAction α β] {A : Set β} {a : α} {x : β},
  x ∈ -a +ᵥ A ↔ a +ᵥ x ∈ A

Defined in: Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
Cited by: 5 results in Mathlib
Foundations: Depth 12 from the axioms · uses propext, Quot.sound
Assumes: AddGroup AddAction

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
AddGroupstatement and proof · cited by 4,410
HVAdd.hVAddstatement and proof · cited by 1,820
AddActionstatement and proof · cited by 820
Set.vaddSetstatement · cited by 403
Set.mem_imageproof · cited by 131
neg_vadd_eq_iffproof · cited by 13

Cited by5

Results whose statement or proof uses this declaration.

vadd_singleton_mem_nhds_of_sigmaCompactproof · cited by 1
AddAction.set_mem_fixedBy_iffproof · cited by 1
AddAction.set_mem_fixedBy_of_movedBy_subsetproof · cited by 1
MeasureTheory.pairwise_disjoint_addFundamentalInteriorproof · cited by 0
AddAction.set_mem_fixedBy_of_subset_fixedByproof · cited by 0