theorem Th40:
  a in X & X is_less_than a implies "\/"(X,C) = a
proof
  assume that
A1: a in X and
A2: X is_less_than a;
A3: "\/"(X,C) [= a by A2,Def21;
  a [= "\/"(X,C) by A1,Th38;
  hence thesis by A3,LATTICES:8;
end;
