0 / 2 < PI / 2 by XREAL_1:74;
then (PI / 2) * (- 1) < 0 * (- 1) by XREAL_1:69;
then A1: (- (PI / 2)) + ((2 * PI) * 0) < PI / 4 ;
PI / 4 < (PI / 2) + ((2 * PI) * 0) by XREAL_1:76;
hence cos (PI / 4) > 0 by A1, SIN_COS6:13; :: thesis: verum