reserve x, y, X for set;
reserve E for non empty set;
reserve e for Element of E;
reserve u, u1, v, v1, v2, w, w9, w1, w2 for Element of E^omega;
reserve F for Subset of E^omega;
reserve i, k, l for Nat;
reserve TS for non empty transition-system over F;
reserve S, T for Subset of TS;

theorem
  for a, b being FinSequence holds a ^ b = a or b ^ a = a implies b = {}
proof
  let a, b be FinSequence such that
A1: a ^ b = a or b ^ a = a;
  per cases by A1;
  suppose
A2: a ^ b = a;
    len(a ^ b) = len(a) + len(b) by FINSEQ_1:22;
    hence thesis by A2;
  end;
  suppose
A3: b ^ a = a;
    len(b ^ a) = len(b) + len(a) by FINSEQ_1:22;
    hence thesis by A3;
  end;
end;
