reserve n for Nat;

theorem Th16:
  for f being FinSequence st f is one-to-one holds f is weakly-one-to-one
proof
  let f be FinSequence;
  assume
A1: f is one-to-one;
  for i be Nat st 1 <= i & i < len f holds f.i <> f.(i+1)
  proof
    let i be Nat;
    assume that
A2: 1 <= i and
A3: i < len f;
A4: i+1 in dom f by A2,A3,MSUALG_8:1;
A5: i <> i+1;
    i in dom f by A2,A3,MSUALG_8:1;
    hence thesis by A1,A4,A5;
  end;
  hence thesis;
end;
