reserve r,r1,r2, s,x for Real,
  i for Integer;

theorem Th58:
  sin | [.PI/2+2*PI*i,3/2*PI+2*PI*i.] is one-to-one
proof
  set Q = [.PI/2+2*PI*i,3/2*PI+2*PI*i.];
  sin|Q is decreasing by Th54;
  hence thesis by FCONT_3:8;
end;
