deffunc H₁( Nat) -> Subset of X = meet (F ^\ $1);
consider f being SetSequence of X such that
A1: for n being Element of NAT holds f . n = H₁(n) from FUNCT_2:sch 4();
take Union f ; :: thesis: ex f being SetSequence of X st
( Union f = Union f & ( for n being Nat holds f . n = meet (F ^\ n) ) )
take f ; :: thesis: ( Union f = Union f & ( for n being Nat holds f . n = meet (F ^\ n) ) )
thus Union f = Union f ; :: thesis: for n being Nat holds f . n = meet (F ^\ n)
let n be Nat; :: thesis: f . n = meet (F ^\ n)
n in NAT by ORDINAL1:def 12;
hence f . n = meet (F ^\ n) by A1; :: thesis: verum