deffunc H₁( Element of ) -> Subset of = FreeSort X,$1;
consider f being Function such that
A1: ( dom f = the carrier of S & ( for d being Element of holds f . d = H₁(d) ) ) from FUNCT_1:sch 4();
reconsider f = f as ManySortedSet of the carrier of S by A1, PARTFUN1:def 4, RELAT_1:def 18;
take f ; :: thesis: for s being SortSymbol of holds f . s = FreeSort X,s
thus for s being SortSymbol of holds f . s = FreeSort X,s by A1; :: thesis: verum