reserve i,j for Nat;

theorem Th4:
  for C being ConstructorSignature st C is standardized
  for o being OperSymbol of C
  holds o is constructor iff o in Constructors
  proof
    let C be ConstructorSignature such that
A1: C is standardized;
    let o be OperSymbol of C;
    thus o is constructor implies o in Constructors by A1;
    assume o in Constructors; then
    not o in {*, non_op} by ABCMIZ_1:39,XBOOLE_0:3;
    hence o <> * & o <> non_op by TARSKI:def 2;
  end;
