PI in ].0,4.[ by SIN_COS:def 28;
then A1: PI > 0 by XXREAL_1:4;
then A2: PI / 4 < PI / 1 by XREAL_1:76;
PI / 4 > 0 / 4 by A1, XREAL_1:74;
hence PI / 4 in ].0,PI.[ by A2, XXREAL_1:4; :: thesis: verum