∀ {α : Type u} {β : Type v} [inst : Ord α] [Std.TransOrd α] [inst_2 : BEq α] [Std.LawfulBEqOrd α]
  {l : List ((_ : α) × β)},
  Std.Internal.List.DistinctKeys l →
    ∀ {k : α} {f : β → β} {he : (Std.Internal.List.Const.modifyKey k f l).isEmpty = false},
      Std.Internal.List.minKey (Std.Internal.List.Const.modifyKey k f l) he =
        if (Std.Internal.List.minKey l ⋯ == k) = true then k else Std.Internal.List.minKey l ⋯