src/HOL/Tools/BNF/bnf_lfp_util.ML

a few new and tidier proofs (mostly about finite sets)

(*  Title:      HOL/Tools/BNF/bnf_lfp_util.ML
    Author:     Dmitriy Traytel, TU Muenchen
    Author:     Jasmin Blanchette, TU Muenchen
    Copyright   2012

Library for the datatype construction.
*)

signature BNF_LFP_UTIL =
sig
  val mk_bij_betw: term -> term -> term -> term
  val mk_cardSuc: term -> term
  val mk_not_empty: term -> term
  val mk_not_eq: term -> term -> term
  val mk_rapp: term -> typ -> term
  val mk_relChain: term -> term -> term
  val mk_underS: term -> term
  val mk_worec: term -> term -> term
end;

structure BNF_LFP_Util : BNF_LFP_UTIL =
struct

open BNF_Util

(*reverse application*)
fun mk_rapp arg T = Term.absdummy (fastype_of arg --> T) (Bound 0 $ arg);

fun mk_underS r =
  let val T = fst (dest_relT (fastype_of r));
  in Const (\<^const_name>\<open>underS\<close>, mk_relT (T, T) --> T --> HOLogic.mk_setT T) $ r end;

fun mk_worec r f =
  let val (A, AB) = apfst domain_type (dest_funT (fastype_of f));
  in Const (\<^const_name>\<open>wo_rel.worec\<close>, mk_relT (A, A) --> (AB --> AB) --> AB) $ r $ f end;

fun mk_relChain r f =
  let val (A, AB) = `domain_type (fastype_of f);
  in Const (\<^const_name>\<open>relChain\<close>, mk_relT (A, A) --> AB --> HOLogic.boolT) $ r $ f end;

fun mk_cardSuc r =
  let val T = fst (dest_relT (fastype_of r));
  in Const (\<^const_name>\<open>cardSuc\<close>, mk_relT (T, T) --> mk_relT (`I (HOLogic.mk_setT T))) $ r end;

fun mk_bij_betw f A B =
 Const (\<^const_name>\<open>bij_betw\<close>,
   fastype_of f --> fastype_of A --> fastype_of B --> HOLogic.boolT) $ f $ A $ B;

fun mk_not_eq x y = HOLogic.mk_not (HOLogic.mk_eq (x, y));

fun mk_not_empty B = mk_not_eq B (HOLogic.mk_set (HOLogic.dest_setT (fastype_of B)) []);

end;