--- a/src/CCL/wfd.ML Mon Jul 17 18:42:38 2006 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,193 +0,0 @@
-(* Title: CCL/Wfd.ML
- ID: $Id$
-*)
-
-(***********)
-
-val [major,prem] = goalw (the_context ()) [Wfd_def]
- "[| Wfd(R); \
-\ !!x.[| ALL y. <y,x>: R --> P(y) |] ==> P(x) |] ==> \
-\ P(a)";
-by (rtac (major RS spec RS mp RS spec RS CollectD) 1);
-by (fast_tac (set_cs addSIs [prem RS CollectI]) 1);
-qed "wfd_induct";
-
-val [p1,p2,p3] = goal (the_context ())
- "[| !!x y.<x,y> : R ==> Q(x); \
-\ ALL x. (ALL y. <y,x> : R --> y : P) --> x : P; \
-\ !!x. Q(x) ==> x:P |] ==> a:P";
-by (rtac (p2 RS spec RS mp) 1);
-by (fast_tac (set_cs addSIs [p1 RS p3]) 1);
-qed "wfd_strengthen_lemma";
-
-fun wfd_strengthen_tac s i = res_inst_tac [("Q",s)] wfd_strengthen_lemma i THEN
- assume_tac (i+1);
-
-val wfd::prems = goal (the_context ()) "[| Wfd(r); <a,x>:r; <x,a>:r |] ==> P";
-by (subgoal_tac "ALL x. <a,x>:r --> <x,a>:r --> P" 1);
-by (fast_tac (FOL_cs addIs prems) 1);
-by (rtac (wfd RS wfd_induct) 1);
-by (ALLGOALS (fast_tac (ccl_cs addSIs prems)));
-qed "wf_anti_sym";
-
-val prems = goal (the_context ()) "[| Wfd(r); <a,a>: r |] ==> P";
-by (rtac wf_anti_sym 1);
-by (REPEAT (resolve_tac prems 1));
-qed "wf_anti_refl";
-
-(*** Irreflexive transitive closure ***)
-
-val [prem] = goal (the_context ()) "Wfd(R) ==> Wfd(R^+)";
-by (rewtac Wfd_def);
-by (REPEAT (ares_tac [allI,ballI,impI] 1));
-(*must retain the universal formula for later use!*)
-by (rtac allE 1 THEN assume_tac 1);
-by (etac mp 1);
-by (rtac (prem RS wfd_induct) 1);
-by (rtac (impI RS allI) 1);
-by (etac tranclE 1);
-by (fast_tac ccl_cs 1);
-by (etac (spec RS mp RS spec RS mp) 1);
-by (REPEAT (atac 1));
-qed "trancl_wf";
-
-(*** Lexicographic Ordering ***)
-
-Goalw [lex_def]
- "p : ra**rb <-> (EX a a' b b'. p = <<a,b>,<a',b'>> & (<a,a'> : ra | a=a' & <b,b'> : rb))";
-by (fast_tac ccl_cs 1);
-qed "lexXH";
-
-val prems = goal (the_context ())
- "<a,a'> : ra ==> <<a,b>,<a',b'>> : ra**rb";
-by (fast_tac (ccl_cs addSIs (prems @ [lexXH RS iffD2])) 1);
-qed "lexI1";
-
-val prems = goal (the_context ())
- "<b,b'> : rb ==> <<a,b>,<a,b'>> : ra**rb";
-by (fast_tac (ccl_cs addSIs (prems @ [lexXH RS iffD2])) 1);
-qed "lexI2";
-
-val major::prems = goal (the_context ())
- "[| p : ra**rb; \
-\ !!a a' b b'.[| <a,a'> : ra; p=<<a,b>,<a',b'>> |] ==> R; \
-\ !!a b b'.[| <b,b'> : rb; p = <<a,b>,<a,b'>> |] ==> R |] ==> \
-\ R";
-by (rtac (major RS (lexXH RS iffD1) RS exE) 1);
-by (REPEAT_SOME (eresolve_tac ([exE,conjE,disjE]@prems)));
-by (ALLGOALS (fast_tac ccl_cs));
-qed "lexE";
-
-val [major,minor] = goal (the_context ())
- "[| p : r**s; !!a a' b b'. p = <<a,b>,<a',b'>> ==> P |] ==>P";
-by (rtac (major RS lexE) 1);
-by (ALLGOALS (fast_tac (set_cs addSEs [minor])));
-qed "lex_pair";
-
-val [wfa,wfb] = goal (the_context ())
- "[| Wfd(R); Wfd(S) |] ==> Wfd(R**S)";
-by (rewtac Wfd_def);
-by (safe_tac ccl_cs);
-by (wfd_strengthen_tac "%x. EX a b. x=<a,b>" 1);
-by (fast_tac (term_cs addSEs [lex_pair]) 1);
-by (subgoal_tac "ALL a b.<a,b>:P" 1);
-by (fast_tac ccl_cs 1);
-by (rtac (wfa RS wfd_induct RS allI) 1);
-by (rtac (wfb RS wfd_induct RS allI) 1);back();
-by (fast_tac (type_cs addSEs [lexE]) 1);
-qed "lex_wf";
-
-(*** Mapping ***)
-
-Goalw [wmap_def]
- "p : wmap(f,r) <-> (EX x y. p=<x,y> & <f(x),f(y)> : r)";
-by (fast_tac ccl_cs 1);
-qed "wmapXH";
-
-val prems = goal (the_context ())
- "<f(a),f(b)> : r ==> <a,b> : wmap(f,r)";
-by (fast_tac (ccl_cs addSIs (prems @ [wmapXH RS iffD2])) 1);
-qed "wmapI";
-
-val major::prems = goal (the_context ())
- "[| p : wmap(f,r); !!a b.[| <f(a),f(b)> : r; p=<a,b> |] ==> R |] ==> R";
-by (rtac (major RS (wmapXH RS iffD1) RS exE) 1);
-by (REPEAT_SOME (eresolve_tac ([exE,conjE,disjE]@prems)));
-by (ALLGOALS (fast_tac ccl_cs));
-qed "wmapE";
-
-val [wf] = goal (the_context ())
- "Wfd(r) ==> Wfd(wmap(f,r))";
-by (rewtac Wfd_def);
-by (safe_tac ccl_cs);
-by (subgoal_tac "ALL b. ALL a. f(a)=b-->a:P" 1);
-by (fast_tac ccl_cs 1);
-by (rtac (wf RS wfd_induct RS allI) 1);
-by (safe_tac ccl_cs);
-by (etac (spec RS mp) 1);
-by (safe_tac (ccl_cs addSEs [wmapE]));
-by (etac (spec RS mp RS spec RS mp) 1);
-by (assume_tac 1);
-by (rtac refl 1);
-qed "wmap_wf";
-
-(* Projections *)
-
-val prems = goal (the_context ()) "<xa,ya> : r ==> <<xa,xb>,<ya,yb>> : wmap(fst,r)";
-by (rtac wmapI 1);
-by (simp_tac (term_ss addsimps prems) 1);
-qed "wfstI";
-
-val prems = goal (the_context ()) "<xb,yb> : r ==> <<xa,xb>,<ya,yb>> : wmap(snd,r)";
-by (rtac wmapI 1);
-by (simp_tac (term_ss addsimps prems) 1);
-qed "wsndI";
-
-val prems = goal (the_context ()) "<xc,yc> : r ==> <<xa,<xb,xc>>,<ya,<yb,yc>>> : wmap(thd,r)";
-by (rtac wmapI 1);
-by (simp_tac (term_ss addsimps prems) 1);
-qed "wthdI";
-
-(*** Ground well-founded relations ***)
-
-val prems = goalw (the_context ()) [wf_def]
- "[| Wfd(r); a : r |] ==> a : wf(r)";
-by (fast_tac (set_cs addSIs prems) 1);
-qed "wfI";
-
-val prems = goalw (the_context ()) [Wfd_def] "Wfd({})";
-by (fast_tac (set_cs addEs [EmptyXH RS iffD1 RS FalseE]) 1);
-qed "Empty_wf";
-
-val prems = goalw (the_context ()) [wf_def] "Wfd(wf(R))";
-by (res_inst_tac [("Q","Wfd(R)")] (excluded_middle RS disjE) 1);
-by (ALLGOALS (asm_simp_tac CCL_ss));
-by (rtac Empty_wf 1);
-qed "wf_wf";
-
-Goalw [NatPR_def] "p : NatPR <-> (EX x:Nat. p=<x,succ(x)>)";
-by (fast_tac set_cs 1);
-qed "NatPRXH";
-
-Goalw [ListPR_def] "p : ListPR(A) <-> (EX h:A. EX t:List(A).p=<t,h$t>)";
-by (fast_tac set_cs 1);
-qed "ListPRXH";
-
-val NatPRI = refl RS (bexI RS (NatPRXH RS iffD2));
-val ListPRI = refl RS (bexI RS (bexI RS (ListPRXH RS iffD2)));
-
-Goalw [Wfd_def] "Wfd(NatPR)";
-by (safe_tac set_cs);
-by (wfd_strengthen_tac "%x. x:Nat" 1);
-by (fast_tac (type_cs addSEs [XH_to_E NatPRXH]) 1);
-by (etac Nat_ind 1);
-by (ALLGOALS (fast_tac (type_cs addEs [XH_to_E NatPRXH])));
-qed "NatPR_wf";
-
-Goalw [Wfd_def] "Wfd(ListPR(A))";
-by (safe_tac set_cs);
-by (wfd_strengthen_tac "%x. x:List(A)" 1);
-by (fast_tac (type_cs addSEs [XH_to_E ListPRXH]) 1);
-by (etac List_ind 1);
-by (ALLGOALS (fast_tac (type_cs addEs [XH_to_E ListPRXH])));
-qed "ListPR_wf";