A1: 0 in ].(- (PI / 2)),(PI / 2).[ ;
A2: {0} c= ].(- (PI / 2)),(PI / 2).[

proof

let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in {0} or x in ].(- (PI / 2)),(PI / 2).[ )
assume x in {0} ; :: thesis: x in ].(- (PI / 2)),(PI / 2).[
hence x in ].(- (PI / 2)),(PI / 2).[ by A1, TARSKI:def 1; :: thesis: verum

end;

].0,(PI / 2).[ c= ].(- (PI / 2)),(PI / 2).[ by XXREAL_1:46;
then ].0,(PI / 2).[ \/ {0} c= ].(- (PI / 2)),(PI / 2).[ by A2, XBOOLE_1:8;
hence [.0,(PI / 2).[ c= ].(- (PI / 2)),(PI / 2).[ by XXREAL_1:131; :: thesis: verum