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
  for f,g,h being strict LModMorphism of R st dom h = cod g & dom g =
  cod f holds h*(g*f) = (h*g)*f
proof
  let f,g,h be strict LModMorphism of R such that
A1: dom h = cod g and
A2: dom g = cod f;
  set G2 = cod f, G3 = cod g;
  reconsider h9 = h as strict Morphism of G3,(cod h) by A1,Def8;
  reconsider g9 = g as strict Morphism of G2,G3 by A2,Def8;
  reconsider f9 = f as strict Morphism of (dom f),G2 by Def8;
  h9*(g9*f9) = (h9*g9)*f9 by Th16;
  hence thesis;
end;
