reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;

theorem Th52:
  for f,g being Relation of X,X st rng f = X & rng g = X holds rng (g*f) = X
proof
  let f,g be Relation of X,X;
  assume that
A1: rng f = X and
A2: rng g = X;
  thus rng(g*f) = f.:X by A2,RELAT_1:127
    .= X by A1,RELSET_1:22;
end;
