deffunc H₁( Nat) -> Subset of Omega = disjointify g,$1;
consider f being Function of NAT ,(bool Omega) such that
A1: for x being Element of NAT holds f . x = H₁(x) from FUNCT_2:sch 4();
take f ; :: thesis: for n being Nat holds f . n = disjointify g,n
let n be Nat; :: thesis: f . n = disjointify g,n
n in NAT by ORDINAL1:def 13;
hence f . n = disjointify g,n by A1; :: thesis: verum