reserve a,b,c,x,y,z for object,X,Y,Z for set,
  n for Nat,
  i,j for Integer,
  r,r1,r2,r3,s for Real,
  c1,c2 for Complex,
  p for Point of TOP-REAL n;

theorem
  for s being Real holds (Rotate(s)) * (Rotate(-s)) = id TOP-REAL 2
  proof
    let s be Real;
    let p be Point of T2;
    set f = Rotate(s);
    set g = Rotate(-s);
    thus (f*g).p = f.(g.p) by FUNCT_2:15
    .= p by Th46
    .= (id T2).p;
  end;
