
theorem
  for C being Category, I being (Indexing of C), T being TargetCat of I
  holds (I-functor(C,T))-indexing_of C = I
proof
  let C be Category, I be Indexing of C;
  let T be TargetCat of I;
  set F = I-functor(C,T);
A1: ex f being (ManySortedSet of the carrier of C), g being ManySortedSet of
  the carrier' of C st I = [f,g] by Def4;
  thus F-indexing_of C = [I`1, pr2 F] by Lm3
    .= [I`1, I`2] by Th20
    .= I by A1;
end;
