reserve a, b, c, d, x, y, z for Complex;
reserve r for Real;

theorem
  a <> 0 & b <> 0 implies angle(a,b) = angle(-a,-b)
proof
  assume a <> 0 & b <> 0;
  hence angle(a,b) = angle(Rotate(a,PI),Rotate(b,PI)) by Th63
    .= angle(-a,Rotate(b,PI)) by Th58
    .= angle(-a,-b) by Th58;
end;
