reserve D,D9 for non empty set;
reserve R for Ring;
reserve G,H,S for non empty ModuleStr over R;
reserve UN for Universe;
reserve R for Ring;
reserve G, H for LeftMod of R;
reserve G1, G2, G3 for LeftMod of R;
reserve f for LModMorphismStr over R;

theorem Th13:
  for G being Morphism of G2,G3, F being Morphism of G1,G2, g
being Function of G2,G3, f being Function of G1,G2 st G = LModMorphismStr(#G2,
G3,g#) & F = LModMorphismStr(#G1,G2,f#) holds G*'F = LModMorphismStr(#G1,G3,g*f
  #) & G*F = LModMorphismStr(# G1,G3,g*f#)
proof
  let G be Morphism of G2,G3, F be Morphism of G1,G2, g be Function of G2,G3,
  f be Function of G1,G2 such that
A1: G = LModMorphismStr(#G2,G3,g#) & F = LModMorphismStr(#G1,G2,f#);
  dom(G) = G2 by Def8
    .= cod(F) by Def8;
  hence thesis by A1,Def10;
end;
