reserve n for Nat;

theorem Th3:
  for x be VECTOR of REAL-NS n, y be Element of REAL n, a be Real
 st x=y holds a * x = a * y
proof
  let x be Point of REAL-NS n, y be Element of REAL n, a be Real;
  assume
A1: x = y;
  reconsider a as Real;
  a * x =(Euclid_mult n).(a,x) by Def4
    .=a*y by A1,Def2;
  hence thesis;
end;
