(* Title: HOLCF/Dnat.ML
ID: $Id$
Author: Franz Regensburger
Copyright 1993, 1995 Technische Universitaet Muenchen
*)
open Dnat;
(* ------------------------------------------------------------------------- *)
(* expand fixed point properties *)
(* ------------------------------------------------------------------------- *)
bind_thm ("iterator_def2", fix_prover2 Dnat.thy iterator_def
"iterator = (LAM n f x. case n of dzero => x | \
\ dsucc`m => f`(iterator`m`f`x))");
(* ------------------------------------------------------------------------- *)
(* recursive properties *)
(* ------------------------------------------------------------------------- *)
qed_goal "iterator1" Dnat.thy "iterator`UU`f`x = UU"
(fn prems =>
[
(stac iterator_def2 1),
(simp_tac (HOLCF_ss addsimps dnat.rews) 1)
]);
qed_goal "iterator2" Dnat.thy "iterator`dzero`f`x = x"
(fn prems =>
[
(stac iterator_def2 1),
(simp_tac (HOLCF_ss addsimps dnat.rews) 1)
]);
qed_goal "iterator3" Dnat.thy
"n~=UU ==> iterator`(dsucc`n)`f`x = f`(iterator`n`f`x)"
(fn prems =>
[
(cut_facts_tac prems 1),
(rtac trans 1),
(stac iterator_def2 1),
(asm_simp_tac (HOLCF_ss addsimps dnat.rews) 1),
(rtac refl 1)
]);
val iterator_rews =
[iterator1, iterator2, iterator3];
val dnat_flat = prove_goal Dnat.thy "!x y::dnat. x<<y --> x=UU | x=y"
(fn _ => [
(rtac allI 1),
(res_inst_tac [("x","x")] dnat.ind 1),
(fast_tac HOL_cs 1),
(rtac allI 1),
(res_inst_tac [("x","y")] dnat.casedist 1),
(fast_tac (HOL_cs addSIs [UU_I]) 1),
(Asm_simp_tac 1),
(asm_simp_tac (simpset() addsimps dnat.dist_les) 1),
(rtac allI 1),
(res_inst_tac [("x","y")] dnat.casedist 1),
(fast_tac (HOL_cs addSIs [UU_I]) 1),
(asm_simp_tac (simpset() addsimps dnat.dist_les) 1),
(asm_simp_tac (simpset() addsimps dnat.rews) 1),
(strip_tac 1),
(subgoal_tac "d<<da" 1),
(etac allE 1),
(dtac mp 1),
(atac 1),
(etac disjE 1),
(contr_tac 1),
(Asm_simp_tac 1),
(resolve_tac dnat.inverts 1),
(REPEAT (atac 1))]);