theorem
  "\/"(X,C) = "/\"({a: a is_greater_than X}, C)
proof
  set Y = {a: a is_greater_than X};
A1: "\/"(X,C) is_less_than Y
  proof
    let a;
    assume a in Y;
    then ex b st a = b & b is_greater_than X;
    hence thesis by Def21;
  end;
  X is_less_than "\/"(X,C) by Def21;
  then "\/"(X,C) in Y;
  then for b st b is_less_than Y holds b [= "\/"(X,C);
  hence thesis by A1,Th34;
end;
