reserve V for non empty set,
  A,B,A9,B9 for Element of V;
reserve f,f9 for Element of Funcs(V);
reserve m,m1,m2,m3,m9 for Element of Maps V;
reserve a,b for Object of Ens(V);
reserve f,g,f1,f2 for Morphism of Ens(V);

theorem Th27:
  dom g = cod f implies g(*)f = (@g)*(@f)
proof
  assume
A1: dom g = cod f;
  then dom(@g) = cod f by Def9;
  then
A2: dom(@g) = cod(@f) by Def10;
  thus g(*)f = (the Comp of Ens(V)).(@g,f) by A1,CAT_1:16
    .= (@g)*(@f) by A2,Def11;
end;
