reserve n for Nat;

theorem Th3:
  for D be non empty set for f be FinSequence of D for G be Matrix
of D for p be Element of D st p in rng f holds f is_sequence_on G implies f:-p
  is_sequence_on G
proof
  let D be non empty set;
  let f be FinSequence of D;
  let G be Matrix of D;
  let p be Element of D;
  assume that
A1: p in rng f and
A2: f is_sequence_on G;
  ex i be Element of NAT st i+1 = p..f & f:-p = f/^i by A1,FINSEQ_5:49;
  hence thesis by A2,JORDAN8:2;
end;
