Moved well_ord_Memrel, lt_eq_pred, Ord_iso_implies_eq_lemma, Ord_iso_implies_eq to top of file, as they do not require the other material. Simplified proof of ordertype_subset. Proved ordertype_eq: a short proof using deepen_tac! Deleted bij_ordermap_vimage and ordermap_Memrel "bij_ordermap_vimage and ordermap_Memrelf. [| f: bij(A,B); well_ord(B,r); x:A |] ==>\ \ ordermap(A,rvimage(A,f,r)) ` x = ordermap(B,r) ` (f`x)"; "\ ordermap(A,rvimage(A,f,r)) ` x = ordermap(B,r) ` (f`x)";i. [| Ord(i); j:i |] ==> ordermap(i,Memrel(i)) ` j = j" because ordertype_eq serves the same purpose. Proofs of bij_ordertype_vimage and ordertype_Memrel are now trivial.

qed is a utility that makes ML files store the defined theories in Isabelle's theorem database