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 Th42:
  for s being Real, p being Point of TOP-REAL 2 holds
  Arg((Rotate(s)).p) = Arg Rotate(euc2cpx(p),s)
  proof
    let s be Real;
    let p be Point of T2;
    (Rotate(s)).p = cpx2euc(Rotate(euc2cpx(p),s)) by JORDAN24:def 3;
    hence thesis by EUCLID_3:1;
  end;
