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