reserve B,C,D for Category;

theorem Th16:
  for f,g being Morphism of C opp st dom g = cod f holds opp (g(*)f)
  = (opp f)(*)(opp g)
proof
  let f,g be Morphism of C opp;
  assume
A1: dom g = cod f;
A2: cod(opp g) = dom g & dom(opp f) = cod f;
  then
A3: [opp f,opp g] in dom( the Comp of C ) by A1,CAT_1:15;
  thus opp (g(*)f) = ~(the Comp of C).(opp g,opp f) by A1,CAT_1:16
    .= (the Comp of C).(opp f,opp g) by A3,FUNCT_4:def 2
    .= (opp f)(*)(opp g) by A1,A2,CAT_1:16;
end;
