theorem Th49:
  (for y being Element of Y holds g.y = F.(f.y,x)) implies g = F
  [:](f,x)
proof
  assume
A1: for y being Element of Y holds g.y = F.(f.y,x);
  now
    let y be Element of Y;
    thus g.y = F.(f.y,x) by A1
      .= (F[:](f,x)).y by Th48;
  end;
  hence thesis by FUNCT_2:63;
end;
