let i be Integer; :: thesis: cos | [.((2 * PI) * i),(PI + ((2 * PI) * i)).] is one-to-one
set Q1 = [.((2 * PI) * i),(PI + ((2 * PI) * i)).];
cos | [.((2 * PI) * i),(PI + ((2 * PI) * i)).] is decreasing by Th55;
hence cos | [.((2 * PI) * i),(PI + ((2 * PI) * i)).] is one-to-one by FCONT_3:8; :: thesis: verum