reserve n for Nat;

theorem Th4:
  for x be VECTOR of REAL-NS n, a be Element of REAL n st x=a holds -x = -a
proof
  let x be VECTOR of REAL-NS n;
  let a be Element of REAL n;
  assume
A1: x=a;
  reconsider a1=a as Element of n-tuples_on REAL by EUCLID:def 1;
  -x = (-1)*x by RLVECT_1:16
    .=-a1 by A1,Th3;
  hence thesis;
end;
