∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.ExtTreeMap α β cmp} [inst : Std.TransCmp cmp]
  [inst_1 : Inhabited α], t ≠ ∅ → ∀ {km : α}, t.minKey! = km ↔ t.getKey? km = some km ∧ ∀ k ∈ t, (cmp km k).isLE = true