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 Th7:
  for F being Morphism of G,H ex f being Function of G,H st the
  LModMorphismStr of F = LModMorphismStr(#G,H,f#) & f is additive homogeneous
proof
  let F be Morphism of G,H;
A1: the Cod of F = cod(F) .= H by Def8;
A2: the Dom of F = dom(F) .= G by Def8;
  then reconsider f = the Fun of F as Function of G,H by A1;
  take f;
  thus thesis by A2,A1,Th4;
end;
