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 GroupMorphismStr, G1,G2 being AddGroup, f0 being Function
  of G1,G2 st f = GroupMorphismStr(# G1,G2,f0#) holds dom f = G1 & cod f = G2 &
  fun f = f0;
