∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.ExtDTreeMap α β cmp} [inst : Std.TransCmp cmp]
  [inst_1 : Std.LawfulEqCmp cmp] [Inhabited α] {k : α} {f : Option (β k) → Option (β k)} {hc : k ∈ t.alter k f},
  (t.alter k f).getKey k hc = k