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 Th11:
  for g,f being LModMorphism of R st dom(g) = cod(f) ex G1,G2,G3
  st g is Morphism of G2,G3 & f is Morphism of G1,G2
proof
  defpred P[LModMorphism of R,LModMorphism of R] means dom($1) = cod($2);
  let g,f be LModMorphism of R such that
A1: P[g,f];
  consider G2,G3 such that
A2: g is Morphism of G2,G3 by Th9;
A3: G2 = dom(g) by A2,Def8;
  consider G1,G2 being LeftMod of R such that
A4: f is Morphism of G1,G2 by Th9;
  G2 = cod(f) by A4,Def8;
  hence thesis by A1,A2,A3,A4;
end;
