theorem Th7:
  X is linearly-independent & Carrier KL1 c= X & Carrier KL2 c= X
  & a <> 0.INT.Ring & Sum KL1 = a * Sum KL2 implies KL1 = a * KL2
  proof
    assume that
    A1: X is linearly-independent & Carrier KL1 c= X and
    A2: Carrier KL2 c= X & a <> 0.INT.Ring & Sum(KL1) = a * Sum(KL2);
    Carrier(a * KL2) c= X & Sum(KL1) = Sum(a * KL2)
    by A2,ZMODUL02:29, ZMODUL02:53;
    hence thesis by A1,Th5;
  end;
