defpred S₁[ object ] means $1 is XFinSequence of D;
consider X being set such that
A1: for x being object holds
( x in X iff ( x in bool [:NAT,D:] & S₁[x] ) ) from XBOOLE_0:sch 1();
take X ; :: thesis: for x being object holds
( x in X iff x is XFinSequence of D )
let x be object ; :: thesis: ( x in X iff x is XFinSequence of D )
thus ( x in X implies x is XFinSequence of D ) by A1; :: thesis: ( x is XFinSequence of D implies x in X )
assume x is XFinSequence of D ; :: thesis: x in X
then reconsider p = x as XFinSequence of D ;
reconsider p = p as PartFunc of NAT,D by Th11;
p c= [:NAT,D:] ;
hence x in X by A1; :: thesis: verum