∀ {G : Type u_2} {X : Type u_1} {ιₚ : Type u_3} [inst : Group G] [inst_1 : MulAction G X]
  {ps : DiscreteTiling.Protoset G X ιₚ} (pt : DiscreteTiling.PlacedTile ps) (a b : G),
  (QuotientGroup.leftRel (Subgroup.map (MulAction.stabilizer G ↑(↑ps pt.index)).subtype (↑ps pt.index).symmetries)) a
      b →
    (fun g => g • ↑(↑ps pt.index)) a = (fun g => g • ↑(↑ps pt.index)) b