∀ {typeName : Lean.Name} {idx nargs : ℕ} {typeName_1 : Lean.Name} {idx_1 nargs_1 : ℕ},
  Lean.Meta.RefinedDiscrTree.Key.proj typeName idx nargs =
      Lean.Meta.RefinedDiscrTree.Key.proj typeName_1 idx_1 nargs_1 →
    typeName = typeName_1 ∧ idx = idx_1 ∧ nargs = nargs_1