let F be ext-real-membered set ; :: thesis: for f being ext-real number holds f /// F = { (f / w) where w is Element of ExtREAL : w in F }
let f be ext-real number ; :: thesis: f /// F = { (f / w) where w is Element of ExtREAL : w in F }
thus f /// F c= { (f / w) where w is Element of ExtREAL : w in F } :: according to XBOOLE_0:def 10 :: thesis: { (f / w) where w is Element of ExtREAL : w in F } c= f /// F

proof

let e be set ; :: according to TARSKI:def 3 :: thesis: ( not e in f /// F or e in { (f / w) where w is Element of ExtREAL : w in F } )
assume e in f /// F ; :: thesis: e in { (f / w) where w is Element of ExtREAL : w in F }
then consider w1, w2 being Element of ExtREAL such that
A1: e = w1 * w2 and
A2: w1 in {f} and
A3: w2 in F "" ;
consider w3 being Element of ExtREAL such that
A4: w2 = w3 " and
A5: w3 in F by A3;
A6: w1 * (w3 " ) = w1 / w3 ;
w1 = f by A2, TARSKI:def 1;
hence e in { (f / w) where w is Element of ExtREAL : w in F } by A1, A4, A5, A6; :: thesis: verum

end;

let e be set ; :: according to TARSKI:def 3 :: thesis: ( not e in { (f / w) where w is Element of ExtREAL : w in F } or e in f /// F )
assume e in { (f / w) where w is Element of ExtREAL : w in F } ; :: thesis: e in f /// F
then ex w being Element of ExtREAL st
( e = f / w & w in F ) ;
hence e in f /// F by Th216; :: thesis: verum