theorem
  a = "\/"({b: b [= a}, C) & a = "/\"({c: a [= c}, C)
proof
  set X = {b: b [= a}, Y = {c: a [= c};
A1: a in X;
A2: a in Y;
  X is_less_than a
  proof
    let b;
    assume b in X;
    then ex c st b = c & c [= a;
    hence thesis;
  end;
  hence a = "\/"(X,C) by A1,Th40;
  a is_less_than Y
  proof
    let b;
    assume b in Y;
    then ex c st b = c & a [= c;
    hence thesis;
  end;
  hence thesis by A2,Th41;
end;
