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

theorem Th57:
  sin | [.-PI/2+2*PI*i,PI/2+2*PI*i.] is one-to-one
proof
  set Q = [.-PI/2+2*PI*i,PI/2+2*PI*i.];
  sin|Q is increasing by Th53;
  hence thesis by FCONT_3:8;
end;
