ex/pl.ML

--- a/ex/pl.ML	Tue Mar 22 08:26:25 1994 +0100
+++ b/ex/pl.ML	Tue Mar 22 08:28:31 1994 +0100
@@ -1,10 +1,9 @@
-(*  Title: 	HOL/ex/prop-log.ML
+(*  Title: 	HOL/ex/pl.ML
     ID:         $Id$
     Author: 	Tobias Nipkow & Lawrence C Paulson
-    Copyright   1993  TU Muenchen & University of Cambridge
+    Copyright   1994  TU Muenchen & University of Cambridge
 
-For ex/prop-log.thy.  Inductive definition of propositional logic.
-Soundness and completeness w.r.t. truth-tables.
+Soundness and completeness of propositional logic w.r.t. truth-tables.
 
 Prove: If H|=p then G|=p where G:Fin(H)
 *)
@@ -136,7 +135,8 @@
 
 (** The function eval **)
 
-val pl_ss = set_ss addsimps [pl_rec_var,pl_rec_false,pl_rec_imp];
+val pl_ss = set_ss addsimps [pl_rec_var,pl_rec_false,pl_rec_imp]
+                            @ PL0.inject @ PL0.ineq;
 
 goalw PL.thy [eval_def] "tt[false] = False";
 by (simp_tac pl_ss 1);
@@ -213,8 +213,7 @@
 (*This formulation is required for strong induction hypotheses*)
 goal PL.thy "hyps(p,tt) |- if(tt[p], p, p->false)";
 by (rtac (expand_if RS iffD2) 1);
-by(res_inst_tac[("x","p")]spec 1);
-by (rtac pl_ind 1);
+by(PL0.induct_tac "p" 1);
 by (ALLGOALS (simp_tac (pl_ss addsimps [conseq_I, conseq_H])));
 by (fast_tac (set_cs addIs [weaken_left_Un1, weaken_left_Un2, 
 			   weaken_right, imp_false]
@@ -250,25 +249,24 @@
 
 (*For the case hyps(p,t)-insert(#v,Y) |- p;
   we also have hyps(p,t)-{#v} <= hyps(p, t-{v}) *)
-goal PL.thy "!p.hyps(p, t-{v}) <= insert((#v)->false, hyps(p,t)-{#v})";
-by (rtac pl_ind 1);
+goal PL.thy "hyps(p, t-{v}) <= insert((#v)->false, hyps(p,t)-{#v})";
+by (PL0.induct_tac "p" 1);
 by (simp_tac pl_ss 1);
 by (simp_tac (pl_ss setloop (split_tac [expand_if])) 1);
-by (fast_tac (set_cs addSEs [sym RS var_neq_imp] addSDs [var_inject]) 1);
 by (simp_tac pl_ss 1);
 by (fast_tac set_cs 1);
-val hyps_Diff = result() RS spec;
+val hyps_Diff = result();
 
 (*For the case hyps(p,t)-insert(#v -> false,Y) |- p;
   we also have hyps(p,t)-{(#v)->false} <= hyps(p, insert(v,t)) *)
-goal PL.thy "!p.hyps(p, insert(v,t)) <= insert(#v, hyps(p,t)-{(#v)->false})";
-by (rtac pl_ind 1);
+goal PL.thy "hyps(p, insert(v,t)) <= insert(#v, hyps(p,t)-{(#v)->false})";
+by (PL0.induct_tac "p" 1);
 by (simp_tac pl_ss 1);
-by (simp_tac (pl_ss setloop (split_tac [expand_if])) 1);
-by (fast_tac (set_cs addSEs [var_neq_imp, imp_inject] addSDs [var_inject]) 1);
+by (simp_tac (pl_ss addsimps [insert_subset]
+                    setloop (split_tac [expand_if])) 1);
 by (simp_tac pl_ss 1);
 by (fast_tac set_cs 1);
-val hyps_insert = result() RS spec;
+val hyps_insert = result();
 
 (** Two lemmas for use with weaken_left **)
 
@@ -282,11 +280,11 @@
 
 (*The set hyps(p,t) is finite, and elements have the form #v or #v->false;
  could probably prove the stronger hyps(p,t) : Fin(hyps(p,{}) Un hyps(p,nat))*)
-goal PL.thy "!p.hyps(p,t) : Fin(UN v:{x.True}. {#v, (#v)->false})";
-by (rtac pl_ind 1);
+goal PL.thy "hyps(p,t) : Fin(UN v:{x.True}. {#v, (#v)->false})";
+by (PL0.induct_tac "p" 1);
 by (ALLGOALS (simp_tac (pl_ss setloop (split_tac [expand_if])) THEN'
               fast_tac (set_cs addSIs [Fin_0I, Fin_insertI, Fin_UnI])));
-val hyps_finite = result() RS spec;
+val hyps_finite = result();
 
 val Diff_weaken_left = subset_refl RSN (2, Diff_mono) RS weaken_left;
 
@@ -341,4 +339,3 @@
 
 writeln"Reached end of file.";
 
-