reserve n for Nat;

theorem Th2:
  for n be Nat for x,y be VECTOR of REAL-NS n, a,b be
  Element of REAL n st x=a & y=b holds x+y = a + b
proof
  let n be Nat;
  let x,y be VECTOR of REAL-NS n;
  let a,b be Element of REAL n;
  assume x=a & y=b;
  hence x+y = (Euclid_add n).(a,b) by Def4
    .= a+b by Def1;
end;
