reserve x,y,z for set;
reserve f,f1,f2,f3 for FinSequence,
  p,p1,p2,p3 for set,
  i,k for Nat;
reserve D for non empty set,
  p,p1,p2,p3 for Element of D,
  f,f1,f2 for FinSequence of D;

theorem Th89:
  Rotate(f,f/.1) = f
proof
A1: len<*f/.1*> = 1 by FINSEQ_1:39;
  per cases;
  suppose
A2: f is non empty;
    then f/.1 in rng f by Th42;
    hence Rotate(f,f/.1) = (f:-f/.1)^((f-:f/.1)/^1) by Def2
      .= f^((f-:f/.1)/^1) by A2,Th44
      .= f^(<*f/.1*>/^1) by A2,Th44
      .= f^{} by A1,FINSEQ_5:32
      .= f by FINSEQ_1:34;
  end;
  suppose
    f is empty;
    hence thesis by Def2,RELAT_1:38;
  end;
end;
