reserve x for Real;

theorem Th14:
  x in [.PI/2,3/2*PI.] implies cos.x <= 0
proof
  assume x in [.PI/2,3/2*PI.];
  then PI/2 <= x & x <= 3/2*PI by XXREAL_1:1;
  then x = PI/2 or x = 3/2*PI or PI/2 < x & x < 3/2*PI by XXREAL_0:1;
  then x = PI/2 or x = 3/2*PI or x in ].PI/2,3/2*PI.[ by XXREAL_1:4;
  hence thesis by Th13,SIN_COS:76;
end;
