defpred S₁[ object ] means $1 is one-to-one FinSequence 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 set holds
( x in X iff x is one-to-one FinSequence of D )
let x be set ; :: thesis: ( x in X iff x is one-to-one FinSequence of D )
thus ( x in X implies x is one-to-one FinSequence of D ) by A1; :: thesis: ( x is one-to-one FinSequence of D implies x in X )
assume x is one-to-one FinSequence of D ; :: thesis: x in X
then reconsider p = x as one-to-one FinSequence of D ;
p c= [:NAT,D:] ;
hence x in X by A1; :: thesis: verum