∀ {α : Type u} {β : α → Type v} [inst : Ord α] [Std.TransOrd α] [inst_2 : BEq α] [Std.LawfulBEqOrd α]
  {l : List ((a : α) × β a)},
  Std.Internal.List.DistinctKeys l →
    ∀ {k : α},
      (Std.Internal.List.eraseKey k l).isEmpty = false →
        ∀ {fallback : α},
          (compare (Std.Internal.List.minKeyD l fallback)
                (Std.Internal.List.minKeyD (Std.Internal.List.eraseKey k l) fallback)).isLE =
            true