
theorem ThWW:
  for n being Nat
  for a,b,c being Element of TOP-REAL n holds
    c - a - (b - a) = c - b
  proof
    let n be Nat;
    let a,b,c be Element of TOP-REAL n;
    thus c - a - (b - a) = (c - a) - b + a by RLVECT_1:29
        .= c - a + a + - b by RLVECT_1:def 3
        .= c + (- a + a) + - b by RLVECT_1:def 3
        .= c + 0.TOP-REAL n + - b by RLVECT_1:5
        .= c - b;
  end;
