reserve n for Nat;

theorem Th1:
  for x be VECTOR of REAL-NS n, y be Element of REAL n st x=y holds
  ||.x.|| = |.y.|
proof
  let x be VECTOR of REAL-NS n;
  let y be Element of REAL n;
  assume
A1: x=y;
  thus ||.x.|| = (the normF of REAL-NS n).x
    .= (Euclid_norm n).y by A1,Def4
    .= |.y.| by Def3;
end;
