reserve x, x1, x2, y, y1, y2, z, z1, z2 for object, X, X1, X2 for set;
reserve E for non empty set;
reserve e for Element of E;
reserve u, u9, u1, u2, v, v1, v2, w, w1, w2 for Element of E^omega;
reserve F, F1, F2 for Subset of E^omega;
reserve i, k, l, n for Nat;

theorem Th2:
  for p being FinSequence holds p <> {} implies
  ex q being FinSequence, x st p = q^<*x*> & len p = len q + 1
proof
  let p be FinSequence;
  assume p <> {};
  then consider q being FinSequence, x being object such that
A1: p = q^<*x*> by FINSEQ_1:46;
  take q, x;
  len p = len q + len <*x*> by A1,FINSEQ_1:22
    .= len q + 1 by FINSEQ_1:40;
  hence thesis by A1;
end;
