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 being strict LModMorphism of R st dom g = cod f holds dom(g*f)
  = dom f & cod (g*f) = cod g
proof
  let f,g be strict LModMorphism of R;
  assume dom g = cod f;
  then
A1: 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#) by Th14;
  hence dom(g*f) = dom f;
  thus thesis by A1;
end;
