∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap α β cmp} [inst : Std.TransCmp cmp] [Inhabited α]
  {k k' : α} {f : Option β → Option β} {hc : k' ∈ t.alter k f},
  (t.alter k f).getKey k' hc = if heq : cmp k k' = Ordering.eq then k else t.getKey k' ⋯