reserve i,j,e,u for object;
reserve I for set; 
reserve x,X,Y,Z,V for ManySortedSet of I;
reserve I for non empty set,
  x,X,Y for ManySortedSet of I;
reserve I for set,
  x,X,Y,Z for ManySortedSet of I;
reserve X for non-empty ManySortedSet of I;
reserve D for non empty set,
  n for Nat;
reserve X,Y for ManySortedSet of I;

theorem
 for f being Function, M being ManySortedSet of I
   holds (f+*M)|I = M
proof
 let f be Function, M be ManySortedSet of I;
A1: dom(f|I) c= I by RELAT_1:58;
A2: dom M = I by PARTFUN1:def 2;
 thus (f+*M)|I = f|I +* M|I by FUNCT_4:71
   .= f|I +* M
   .= M by A1,A2,FUNCT_4:19;
end;
