reserve x, y for set;
reserve D for non empty set;
reserve UN for Universe;
reserve C for Category;
reserve O for non empty Subset of the carrier of C;
reserve G,H for AddGroup;

theorem Th12:
  for F being Morphism of G,H ex f being Function of G,H st the
  GroupMorphismStr of F = GroupMorphismStr(# G,H,f#) & f is additive
proof
  let F be Morphism of G,H;
A1: the Target of F = cod(F) .= H by Def12;
A2: the Source of F = dom(F) .= G by Def12;
  then reconsider f = the Fun of F as Function of G,H by A1;
  take f;
  thus thesis by A2,A1,Th9;
end;
