A1: PI / 2 < PI / 1 by XREAL_1:76;
then A2: PI / 2 in ].0,PI.[ ;
A3: {(PI / 2)} c= ].0,PI.[

proof

let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in {(PI / 2)} or x in ].0,PI.[ )
assume x in {(PI / 2)} ; :: thesis: x in ].0,PI.[
hence x in ].0,PI.[ by A2, TARSKI:def 1; :: thesis: verum

end;

].0,(PI / 2).[ c= ].0,PI.[ by A1, XXREAL_1:46;
then ].0,(PI / 2).[ \/ {(PI / 2)} c= ].0,PI.[ by A3, XBOOLE_1:8;
hence ].0,(PI / 2).] c= ].0,PI.[ by XXREAL_1:132; :: thesis: verum