defpred S₁[ object ] means $1 is RoughSet of X;
consider F being set such that
A1: for x being object holds
( x in F iff ( x in [:(bool the carrier of X),(bool the carrier of X):] & S₁[x] ) ) from XBOOLE_0:sch 1();
take F ; :: thesis: for x being set holds
( x in F iff x is RoughSet of X )
let x be set ; :: thesis: ( x in F iff x is RoughSet of X )
thus ( x in F implies x is RoughSet of X ) by A1; :: thesis: ( x is RoughSet of X implies x in F )
assume x is RoughSet of X ; :: thesis: x in F
hence x in F by A1; :: thesis: verum