reserve n for Nat;

theorem Th13:
  for D be non empty set for f be FinSequence of D st f is
  poorly-one-to-one circular for p be Element of D holds Rotate(f,p) is
  poorly-one-to-one
proof
  let D be non empty set;
  let f be FinSequence of D;
  assume
A1: f is poorly-one-to-one circular;
  let p be Element of D;
A2: len Rotate(f,p) = len f by FINSEQ_6:179;
  per cases;
  suppose
A3: len f <> 2;
    then f is weakly-one-to-one by A1,Th7;
    then Rotate(f,p) is weakly-one-to-one by A1,Th12;
    hence thesis by A2,A3,Th7;
  end;
  suppose
    len f = 2;
    hence thesis by A2,Def3;
  end;
end;
