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 Th43:
  for s being Real, p being Point of TOP-REAL 2 st p <> 0.TOP-REAL 2
  ex i st Arg((Rotate(s)).p) = s+(Arg p)+2*PI*i
  proof
    let s be Real;
    let p be Point of T2;
    set c = euc2cpx(p);
    assume p <> 0.T2;
    then ex i st Arg(Rotate(c,s)) = 2*PI*i+(s+Arg(c))
    by COMPLEX2:54,EUCLID_3:18;
    hence thesis by Th42;
  end;
