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
  for F being strict GroupMorphism ex G,H being AddGroup, f being
Function of G,H st F is Morphism of G,H & F = GroupMorphismStr(# G,H,f#) & f is
  additive
proof
  let F be strict GroupMorphism;
  consider G,H such that
A1: F is Morphism of G,H by Th14;
  reconsider F9 = F as Morphism of G,H by A1;
  consider f being Function of G,H such that
A2: F9 = GroupMorphismStr(# G,H,f#) & f is additive by Th12;
  take G,H,f;
  thus thesis by A2;
end;
