reserve X,Y,Z for set, x,y,z for object;
reserve i,j for Nat;
reserve A,B,C for Subset of X;
reserve R,R1,R2 for Relation of X;
reserve AX for Subset of [:X,X:];
reserve SFXX for Subset-Family of [:X,X:];
reserve EqR,EqR1,EqR2,EqR3 for Equivalence_Relation of X;
reserve X for non empty set,
  x for Element of X;
reserve F for Part-Family of X;
reserve e,u,v for object, E,X,Y,X1 for set;
reserve X,Y,Z for non empty set;

theorem
  for X,Y,Z for y being Element of Y, F being (Function of X,Y),
      G being Function of Y,Z holds F"{y} c= (G*F)"{G.y}
proof
  let X,Y,Z;
  let y be Element of Y, F be (Function of X,Y), G be Function of Y,Z;
  F"{y} c= (G*F)"Im(G,y) by FUNCT_2:44;
  hence thesis by SETWISEO:8;
end;
