∀ {α : Type u} {β : Type v} {x : BEq α} {x_1 : Hashable α} {m : Std.HashMap α β} [EquivBEq α] [LawfulHashable α]
  {k a fallback : α}, (m.erase k).getKeyD a fallback = if (k == a) = true then fallback else m.getKeyD a fallback