consider G being WEVGraph;
consider G being finite loopless trivial non-multi simple nonnegative-weighted real-WEV WEVGraph;
set F = NAT --> G;
A1: dom (NAT --> G) = NAT by FUNCOP_1:19;
reconsider F = NAT --> G as ManySortedSet of NAT ;

now

let x be Nat; :: thesis: F . x is _Graph
x in NAT by ORDINAL1:def 13;
then F . x in rng F by A1, FUNCT_1:12;
then F . x in {G} by FUNCOP_1:14;
hence F . x is _Graph by TARSKI:def 1; :: thesis: verum

end;

then reconsider F = F as GraphSeq by GLIB_000:def 55;
take F ; :: thesis: ( F is [Weighted] & F is [ELabeled] & F is [VLabeled] )

now

let x be Nat; :: thesis: ( F . x is [Weighted] & F . x is [ELabeled] & F . x is [VLabeled] )
x in NAT by ORDINAL1:def 13;
then F . x in rng F by A1, FUNCT_1:12;
then F . x in {G} by FUNCOP_1:14;
hence ( F . x is [Weighted] & F . x is [ELabeled] & F . x is [VLabeled] ) by TARSKI:def 1; :: thesis: verum

end;

hence ( F is [Weighted] & F is [ELabeled] & F is [VLabeled] ) by Def24, Def25, Def26; :: thesis: verum