reserve a,x,y for object, A,B for set,
  l,m,n for Nat;
reserve X,Y for set, x for object,
  p,q for Function-yielding FinSequence,
  f,g,h for Function;

theorem
  dom f c= X implies compose(<*f*>,X) = f
proof
  compose(<*f*>,X) = f*id X by Th44;
  hence thesis by RELAT_1:51;
end;
