∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.ExtDTreeMap α β cmp} [inst : Std.TransCmp cmp]
  {km : α}, t.minKey? = some km ↔ t.getKey? km = some km ∧ ∀ k ∈ t, (cmp km k).isLE = true