reserve n for Nat;

theorem Th10:
  for f be FinSequence st f is poorly-one-to-one holds Rev f is
  poorly-one-to-one
proof
  let f be FinSequence;
  assume
A1: f is poorly-one-to-one;
A2: len f = len Rev f by FINSEQ_5:def 3;
  per cases;
  suppose
A3: len f <> 2;
    then f is weakly-one-to-one by A1,Th7;
    then Rev f is weakly-one-to-one by Th9;
    hence thesis by A2,A3,Th7;
  end;
  suppose
    len f = 2;
    hence thesis by A2,Def3;
  end;
end;
