
theorem THSD2:
  for n being Nat
  for a,b,c being Element of TOP-REAL n st a - c = b - c holds a = b
  proof
    let n be Nat;
    let a,b,c be Element of TOP-REAL n;
    assume a - c = b - c; then
    a + (-c + c) = b - c + c by RLVECT_1:def 3; then
    a + 0.TOP-REAL n = b - c + c by RLVECT_1:5; then
    a = b + (- c + c) by RLVECT_1:def 3; then
    a = b + 0.TOP-REAL n by RLVECT_1:5;
    hence thesis;
  end;
