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 Th14:
  for f,g being strict LModMorphism of R st dom g = cod f holds ex
  G1,G2,G3 being LeftMod of R, f0 being Function of G1,G2, g0 being Function of
G2,G3 st f = LModMorphismStr(#G1,G2,f0#) & g = LModMorphismStr(#G2,G3,g0#) & g*
  f = LModMorphismStr(#G1,G3,g0*f0#)
proof
  let f,g be strict LModMorphism of R such that
A1: dom g = cod f;
  set G1 = dom f,G2 = cod f, G3 = cod g;
  reconsider f9 = f as strict Morphism of G1,G2 by Def8;
  reconsider g9 = g as strict Morphism of G2,G3 by A1,Def8;
  consider f0 being Function of G1,G2 such that
A2: f9 = LModMorphismStr(#G1,G2,f0#);
  consider g0 being Function of G2,G3 such that
A3: g9 = LModMorphismStr(#G2,G3,g0#) by Th8;
  take G1,G2,G3,f0,g0;
  thus thesis by A2,A3,Th13;
end;
