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 or dom(g*f) c= X implies compose(<*f,g*>,X) = g*f
proof
  compose(<*f,g*>,X) = g*f*id X & g*f*id X = g*(f*id X) by Th50,RELAT_1:36;
  hence thesis by RELAT_1:51;
end;
