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 Th20:
  for f,g being strict GroupMorphism st dom g = cod f holds dom(g*
  f) = dom f & cod (g*f) = cod g
proof
  let f,g be strict GroupMorphism;
  assume dom g = cod f;
  then
A1: ex G1,G2,G3 being AddGroup, f0 being Function of G1,G2, g0 being Function
of G2,G3 st f = GroupMorphismStr(# G1,G2,f0#) & g = GroupMorphismStr(# G2,G3,g0
  #) & g*f = GroupMorphismStr(# G1,G3,g0*f0#) by Th19;
  hence dom(g*f) = dom f;
  thus thesis by A1;
end;
