theorem
  f is invertible implies f" is invertible
proof
  assume
A1: f is invertible;
  then
A2: f*(f") = id b by Def15;
A3: Hom(a,b) <> {} by A1;
  Hom(b,a) <> {} & (f")*f = id a by A1,Def15;
  hence thesis by A3,A2;
end;
