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
  Rotate(<*p1,p2*>,p2) = <*p2,p2*>
proof
  per cases;
  suppose
    p1 = p2;
    hence thesis by Th95;
  end;
  suppose
A1: p1 <> p2;
    rng<*p1,p2*> = {p1,p2} by Lm1;
    then p2 in rng<*p1,p2*> by TARSKI:def 2;
    hence Rotate(<*p1,p2*>,p2) = (<*p1,p2*>:-p2)^((<*p1,p2*>-:p2)/^1) by Def2
      .= <*p2*>^((<*p1,p2*>-:p2)/^1) by A1,Th53
      .= <*p2*>^(<*p1,p2*>/^1) by A1,Th49
      .= <*p2,p2*> by Th46;
  end;
end;
