new theory PPROD
authorpaulson
Mon Nov 16 13:58:56 1998 +0100 (1998-11-16)
changeset 589913d4753079fe
parent 5898 3e34e7aa7479
child 5900 258021e27980
new theory PPROD
src/HOL/UNITY/PPROD.ML
src/HOL/UNITY/PPROD.thy
src/HOL/UNITY/ROOT.ML
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/HOL/UNITY/PPROD.ML	Mon Nov 16 13:58:56 1998 +0100
     1.3 @@ -0,0 +1,385 @@
     1.4 +(*  Title:      HOL/UNITY/PPROD.ML
     1.5 +    ID:         $Id$
     1.6 +    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     1.7 +    Copyright   1998  University of Cambridge
     1.8 +*)
     1.9 +
    1.10 +val rinst = read_instantiate_sg (sign_of thy);
    1.11 +
    1.12 +(*** General lemmas ***)
    1.13 +
    1.14 +Goal "x:C ==> (A Times C <= B Times C) = (A <= B)";
    1.15 +by (Blast_tac 1);
    1.16 +qed "Times_subset_cancel2";
    1.17 +
    1.18 +Goal "x:C ==> (A Times C = B Times C) = (A = B)";
    1.19 +by (blast_tac (claset() addEs [equalityE]) 1);
    1.20 +qed "Times_eq_cancel2";
    1.21 +
    1.22 +Goal "Union(B) Times A = (UN C:B. C Times A)";
    1.23 +by (Blast_tac 1);
    1.24 +qed "Times_Union2";
    1.25 +
    1.26 +Goal "Domain (Union S) = (UN A:S. Domain A)";
    1.27 +by (Blast_tac 1);
    1.28 +qed "Domain_Union";
    1.29 +
    1.30 +(** RTimes: the product of two relations **)
    1.31 +
    1.32 +Goal "(((a,b), (a',b')) : A RTimes B) = ((a,a'):A & (b,b'):B)";
    1.33 +by (simp_tac (simpset() addsimps [RTimes_def]) 1);
    1.34 +qed "mem_RTimes_iff";
    1.35 +AddIffs [mem_RTimes_iff]; 
    1.36 +
    1.37 +Goalw [RTimes_def] "[| A<=C;  B<=D |] ==> A RTimes B <= C RTimes D";
    1.38 +by Auto_tac;
    1.39 +qed "RTimes_mono";
    1.40 +
    1.41 +Goal "{} RTimes B = {}";
    1.42 +by Auto_tac;
    1.43 +qed "RTimes_empty1"; 
    1.44 +
    1.45 +Goal "A RTimes {} = {}";
    1.46 +by Auto_tac;
    1.47 +qed "RTimes_empty2"; 
    1.48 +
    1.49 +Goal "Id RTimes Id = Id";
    1.50 +by Auto_tac;
    1.51 +qed "RTimes_Id"; 
    1.52 +
    1.53 +Addsimps [RTimes_empty1, RTimes_empty2, RTimes_Id]; 
    1.54 +
    1.55 +Goal "Domain (r RTimes s) = Domain r Times Domain s";
    1.56 +by (auto_tac (claset(), simpset() addsimps [Domain_iff]));
    1.57 +qed "Domain_RTimes"; 
    1.58 +
    1.59 +Goal "Range (r RTimes s) = Range r Times Range s";
    1.60 +by (auto_tac (claset(), simpset() addsimps [Range_iff]));
    1.61 +qed "Range_RTimes"; 
    1.62 +
    1.63 +Goal "(r RTimes s) ^^ (A Times B) = r^^A Times s^^B";
    1.64 +by (auto_tac (claset(), simpset() addsimps [Image_iff]));
    1.65 +qed "Image_RTimes"; 
    1.66 +
    1.67 +
    1.68 +Goal "- (UNIV Times A) = UNIV Times (-A)";
    1.69 +by Auto_tac;
    1.70 +qed "Compl_Times_UNIV1"; 
    1.71 +
    1.72 +Goal "- (A Times UNIV) = (-A) Times UNIV";
    1.73 +by Auto_tac;
    1.74 +qed "Compl_Times_UNIV2"; 
    1.75 +
    1.76 +Addsimps [Compl_Times_UNIV1, Compl_Times_UNIV2]; 
    1.77 +
    1.78 +
    1.79 +(**** Lcopy ****)
    1.80 +
    1.81 +(*** Basic properties ***)
    1.82 +
    1.83 +Goal "Init (Lcopy F) = Init F Times UNIV";
    1.84 +by (simp_tac (simpset() addsimps [Lcopy_def]) 1);
    1.85 +qed "Init_Lcopy";
    1.86 +
    1.87 +Goal "Id : (%act. act RTimes Id) `` Acts F";
    1.88 +by (rtac image_eqI 1);
    1.89 +by (rtac Id_in_Acts 2);
    1.90 +by Auto_tac;
    1.91 +val lemma = result();
    1.92 +
    1.93 +Goal "Acts (Lcopy F) = (%act. act RTimes Id) `` Acts F";
    1.94 +by (auto_tac (claset() addSIs [lemma], 
    1.95 +	      simpset() addsimps [Lcopy_def]));
    1.96 +qed "Acts_Lcopy";
    1.97 +
    1.98 +Addsimps [Init_Lcopy];
    1.99 +
   1.100 +Goalw [Lcopy_def, SKIP_def] "Lcopy SKIP = SKIP";
   1.101 +by (rtac program_equalityI 1);
   1.102 +by Auto_tac;
   1.103 +qed "Lcopy_SKIP";
   1.104 +
   1.105 +Addsimps [Lcopy_SKIP];
   1.106 +
   1.107 +
   1.108 +(*** Safety: constrains, stable ***)
   1.109 +
   1.110 +(** In most cases, C = UNIV.  The generalization isn't of obvious value. **)
   1.111 +
   1.112 +Goal "x: C ==> \
   1.113 +\     (Lcopy F : constrains (A Times C) (B Times C)) = (F : constrains A B)";
   1.114 +by (auto_tac (claset(), simpset() addsimps [constrains_def, Lcopy_def]));
   1.115 +by (Blast_tac 1);
   1.116 +qed "Lcopy_constrains";
   1.117 +
   1.118 +Goal "Lcopy F : constrains A B ==> F : constrains (Domain A) (Domain B)";
   1.119 +by (auto_tac (claset(), simpset() addsimps [constrains_def, Lcopy_def]));
   1.120 +by (Blast_tac 1);
   1.121 +qed "Lcopy_constrains_Domain";
   1.122 +
   1.123 +Goal "x: C ==> (Lcopy F : stable (A Times C)) = (F : stable A)";
   1.124 +by (asm_simp_tac (simpset() addsimps [stable_def, Lcopy_constrains]) 1);
   1.125 +qed "Lcopy_stable";
   1.126 +
   1.127 +Goal "(Lcopy F : invariant (A Times UNIV)) = (F : invariant A)";
   1.128 +by (asm_simp_tac (simpset() addsimps [Times_subset_cancel2,
   1.129 +				      invariant_def, Lcopy_stable]) 1);
   1.130 +qed "Lcopy_invariant";
   1.131 +
   1.132 +(** Substitution Axiom versions: Constrains, Stable **)
   1.133 +
   1.134 +Goal "p : reachable (Lcopy F) ==> fst p : reachable F";
   1.135 +by (etac reachable.induct 1);
   1.136 +by (auto_tac
   1.137 +    (claset() addIs reachable.intrs,
   1.138 +     simpset() addsimps [Acts_Lcopy]));
   1.139 +qed "reachable_Lcopy_fst";
   1.140 +
   1.141 +Goal "(a,b) : reachable (Lcopy F) ==> a : reachable F";
   1.142 +by (force_tac (claset() addSDs [reachable_Lcopy_fst], simpset()) 1);
   1.143 +qed "reachable_LcopyD";
   1.144 +
   1.145 +Goal "reachable (Lcopy F) = reachable F Times UNIV";
   1.146 +by (rtac equalityI 1);
   1.147 +by (force_tac (claset() addSDs [reachable_LcopyD], simpset()) 1);
   1.148 +by (Clarify_tac 1);
   1.149 +by (etac reachable.induct 1);
   1.150 +by (ALLGOALS (force_tac (claset() addIs reachable.intrs, 
   1.151 +			 simpset() addsimps [Acts_Lcopy])));
   1.152 +qed "reachable_Lcopy_eq";
   1.153 +
   1.154 +Goal "(Lcopy F : Constrains (A Times UNIV) (B Times UNIV)) =  \
   1.155 +\     (F : Constrains A B)";
   1.156 +by (simp_tac
   1.157 +    (simpset() addsimps [Constrains_def, reachable_Lcopy_eq, 
   1.158 +			 Lcopy_constrains, Sigma_Int_distrib1 RS sym]) 1);
   1.159 +qed "Lcopy_Constrains";
   1.160 +
   1.161 +Goal "(Lcopy F : Stable (A Times UNIV)) = (F : Stable A)";
   1.162 +by (simp_tac (simpset() addsimps [Stable_def, Lcopy_Constrains]) 1);
   1.163 +qed "Lcopy_Stable";
   1.164 +
   1.165 +
   1.166 +(*** Progress: transient, ensures ***)
   1.167 +
   1.168 +Goal "(Lcopy F : transient (A Times UNIV)) = (F : transient A)";
   1.169 +by (auto_tac (claset(),
   1.170 +	      simpset() addsimps [transient_def, Times_subset_cancel2, 
   1.171 +				  Domain_RTimes, Image_RTimes, Lcopy_def]));
   1.172 +qed "Lcopy_transient";
   1.173 +
   1.174 +Goal "(Lcopy F : ensures (A Times UNIV) (B Times UNIV)) = \
   1.175 +\     (F : ensures A B)";
   1.176 +by (simp_tac
   1.177 +    (simpset() addsimps [ensures_def, Lcopy_constrains, Lcopy_transient, 
   1.178 +			 Sigma_Un_distrib1 RS sym, 
   1.179 +			 Sigma_Diff_distrib1 RS sym]) 1);
   1.180 +qed "Lcopy_ensures";
   1.181 +
   1.182 +Goal "F : leadsTo A B ==> Lcopy F : leadsTo (A Times UNIV) (B Times UNIV)";
   1.183 +by (etac leadsTo_induct 1);
   1.184 +by (asm_simp_tac (simpset() addsimps [leadsTo_UN, Times_Union2]) 3);
   1.185 +by (blast_tac (claset() addIs [leadsTo_Trans]) 2);
   1.186 +by (asm_simp_tac (simpset() addsimps [leadsTo_Basis, Lcopy_ensures]) 1);
   1.187 +qed "leadsTo_imp_Lcopy_leadsTo";
   1.188 +
   1.189 +Goal "Lcopy F : ensures A B ==> F : ensures (Domain A) (Domain B)";
   1.190 +by (full_simp_tac
   1.191 +    (simpset() addsimps [ensures_def, Lcopy_constrains, Lcopy_transient, 
   1.192 +			 Domain_Un_eq RS sym,
   1.193 +			 Sigma_Un_distrib1 RS sym, 
   1.194 +			 Sigma_Diff_distrib1 RS sym]) 1);
   1.195 +by (safe_tac (claset() addSDs [Lcopy_constrains_Domain]));
   1.196 +by (etac constrains_weaken_L 1);
   1.197 +by (Blast_tac 1);
   1.198 +(*NOT able to prove this:
   1.199 +Lcopy F : ensures A B ==> F : ensures (Domain A) (Domain B)
   1.200 + 1. [| Lcopy F : transient (A - B);
   1.201 +       F : constrains (Domain (A - B)) (Domain (A Un B)) |]
   1.202 +    ==> F : transient (Domain A - Domain B)
   1.203 +**)
   1.204 +
   1.205 +
   1.206 +Goal "Lcopy F : leadsTo AU BU ==> F : leadsTo (Domain AU) (Domain BU)";
   1.207 +by (etac leadsTo_induct 1);
   1.208 +by (full_simp_tac (simpset() addsimps [Domain_Union]) 3);
   1.209 +by (blast_tac (claset() addIs [leadsTo_UN]) 3);
   1.210 +by (blast_tac (claset() addIs [leadsTo_Trans]) 2);
   1.211 +by (rtac leadsTo_Basis 1);
   1.212 +(*...and so CANNOT PROVE THIS*)
   1.213 +
   1.214 +
   1.215 +(*This also seems impossible to prove??*)
   1.216 +Goal "(Lcopy F : leadsTo (A Times UNIV) (B Times UNIV)) = \
   1.217 +\     (F : leadsTo A B)";
   1.218 +
   1.219 +
   1.220 +
   1.221 +(**** PPROD ****)
   1.222 +
   1.223 +(*** Basic properties ***)
   1.224 +
   1.225 +Goalw [PPROD_def, lift_prog_def]
   1.226 +     "Init (PPROD I F) = {f. ALL i:I. f i : Init F}";
   1.227 +by Auto_tac;
   1.228 +qed "Init_PPROD";
   1.229 +
   1.230 +Goalw [lift_act_def] "lift_act i Id = Id";
   1.231 +by Auto_tac;
   1.232 +qed "lift_act_Id";
   1.233 +Addsimps [lift_act_Id];
   1.234 +
   1.235 +Goalw [lift_act_def]
   1.236 +    "((f,f') : lift_act i act) = (EX s'. f' = f(i := s') & (f i, s') : act)";
   1.237 +by (Blast_tac 1);
   1.238 +qed "lift_act_eq";
   1.239 +AddIffs [lift_act_eq];
   1.240 +
   1.241 +Goal "Acts (PPROD I F) = insert Id (UN i:I. lift_act i `` Acts F)";
   1.242 +by (auto_tac (claset(),
   1.243 +	      simpset() addsimps [PPROD_def, lift_prog_def, Acts_JN]));
   1.244 +qed "Acts_PPROD";
   1.245 +
   1.246 +Addsimps [Init_PPROD];
   1.247 +
   1.248 +Goal "PPROD I SKIP = SKIP";
   1.249 +by (rtac program_equalityI 1);
   1.250 +by (auto_tac (claset(),
   1.251 +	      simpset() addsimps [PPROD_def, lift_prog_def, 
   1.252 +				  SKIP_def, Acts_JN]));
   1.253 +qed "PPROD_SKIP";
   1.254 +
   1.255 +Goal "PPROD {} F = SKIP";
   1.256 +by (simp_tac (simpset() addsimps [PPROD_def]) 1);
   1.257 +qed "PPROD_empty";
   1.258 +
   1.259 +Addsimps [PPROD_SKIP, PPROD_empty];
   1.260 +
   1.261 +Goalw [PPROD_def]  "PPROD (insert i I) F = (lift_prog i F) Join (PPROD I F)";
   1.262 +by Auto_tac;
   1.263 +qed "PPROD_insert";
   1.264 +
   1.265 +
   1.266 +(*** Safety: constrains, stable ***)
   1.267 +
   1.268 +val subsetCE' = rinst
   1.269 +            [("c", "(%u. ?s)(i:=?s')")] subsetCE;
   1.270 +
   1.271 +Goal "i : I ==>  \
   1.272 +\     (PPROD I F : constrains {f. f i : A} {f. f i : B})  =  \
   1.273 +\     (F : constrains A B)";
   1.274 +by (auto_tac (claset(), 
   1.275 +	      simpset() addsimps [constrains_def, lift_prog_def, PPROD_def,
   1.276 +				  Acts_JN]));
   1.277 +by (REPEAT (Blast_tac 2));
   1.278 +by (force_tac (claset() addSEs [subsetCE', allE, ballE], simpset()) 1);
   1.279 +qed "PPROD_constrains";
   1.280 +
   1.281 +Goal "[| PPROD I F : constrains AA BB;  i: I |] \
   1.282 +\     ==> F : constrains (Applyall AA i) (Applyall BB i)";
   1.283 +by (auto_tac (claset(), 
   1.284 +	      simpset() addsimps [Applyall_def, constrains_def, 
   1.285 +				  lift_prog_def, PPROD_def, Acts_JN]));
   1.286 +by (force_tac (claset() addSIs [rinst [("x", "?ff(i := ?u)")] image_eqI]
   1.287 +			addSEs [rinst [("c", "?ff(i := ?u)")] subsetCE, ballE],
   1.288 +	       simpset()) 1);
   1.289 +qed "PPROD_constrains_projection";
   1.290 +
   1.291 +
   1.292 +Goal "i : I ==> (PPROD I F : stable {f. f i : A}) = (F : stable A)";
   1.293 +by (asm_simp_tac (simpset() addsimps [stable_def, PPROD_constrains]) 1);
   1.294 +qed "PPROD_stable";
   1.295 +
   1.296 +Goal "i : I ==> (PPROD I F : invariant {f. f i : A}) = (F : invariant A)";
   1.297 +by (auto_tac (claset(),
   1.298 +	      simpset() addsimps [invariant_def, PPROD_stable]));
   1.299 +qed "PPROD_invariant";
   1.300 +
   1.301 +
   1.302 +(** Substitution Axiom versions: Constrains, Stable **)
   1.303 +
   1.304 +Goal "[| f : reachable (PPROD I F);  i : I |] ==> f i : reachable F";
   1.305 +by (etac reachable.induct 1);
   1.306 +by (auto_tac
   1.307 +    (claset() addIs reachable.intrs,
   1.308 +     simpset() addsimps [Acts_PPROD]));
   1.309 +qed "reachable_PPROD";
   1.310 +
   1.311 +Goal "reachable (PPROD I F) <= {f. ALL i:I. f i : reachable F}";
   1.312 +by (force_tac (claset() addSDs [reachable_PPROD], simpset()) 1);
   1.313 +qed "reachable_PPROD_subset1";
   1.314 +
   1.315 +Goal "[| i ~: I;  A : reachable F |]     \
   1.316 +\  ==> ALL f. f : reachable (PPROD I F)  \
   1.317 +\             --> f(i:=A) : reachable (lift_prog i F Join PPROD I F)";
   1.318 +by (etac reachable.induct 1);
   1.319 +by (ALLGOALS Clarify_tac);
   1.320 +by (etac reachable.induct 1);
   1.321 +(*Init, Init case*)
   1.322 +by (force_tac (claset() addIs reachable.intrs,
   1.323 +	       simpset() addsimps [lift_prog_def]) 1);
   1.324 +(*Init of F, action of PPROD F case*)
   1.325 +br reachable.Acts 1;
   1.326 +by (force_tac (claset(), simpset() addsimps [Acts_Join]) 1);
   1.327 +ba 1;
   1.328 +by (force_tac (claset() addIs [ext], simpset() addsimps [Acts_PPROD]) 1);
   1.329 +(*induction over the 2nd "reachable" assumption*)
   1.330 +by (eres_inst_tac [("xa","f")] reachable.induct 1);
   1.331 +(*Init of PPROD F, action of F case*)
   1.332 +by (res_inst_tac [("act","lift_act i act")] reachable.Acts 1);
   1.333 +by (force_tac (claset(), simpset() addsimps [lift_prog_def, Acts_Join]) 1);
   1.334 +by (force_tac (claset() addIs [reachable.Init], simpset()) 1);
   1.335 +by (force_tac (claset() addIs [ext], simpset() addsimps [lift_act_def]) 1);
   1.336 +(*last case: an action of PPROD I F*)
   1.337 +br reachable.Acts 1;
   1.338 +by (force_tac (claset(), simpset() addsimps [Acts_Join]) 1);
   1.339 +ba 1;
   1.340 +by (force_tac (claset() addIs [ext], simpset() addsimps [Acts_PPROD]) 1);
   1.341 +qed_spec_mp "reachable_lift_Join_PPROD";
   1.342 +
   1.343 +
   1.344 +(*The index set must be finite: otherwise infinitely many copies of F can
   1.345 +  perform actions, and PPROD can never catch up in finite time.*)
   1.346 +Goal "finite I ==> {f. ALL i:I. f i : reachable F} <= reachable (PPROD I F)";
   1.347 +by (etac finite_induct 1);
   1.348 +by (Simp_tac 1);
   1.349 +by (force_tac (claset() addDs [reachable_lift_Join_PPROD], 
   1.350 +	       simpset() addsimps [PPROD_insert]) 1);
   1.351 +qed "reachable_PPROD_subset2";
   1.352 +
   1.353 +Goal "finite I ==> reachable (PPROD I F) = {f. ALL i:I. f i : reachable F}";
   1.354 +by (REPEAT_FIRST (ares_tac [equalityI,
   1.355 +			    reachable_PPROD_subset1, 
   1.356 +			    reachable_PPROD_subset2]));
   1.357 +qed "reachable_PPROD_eq";
   1.358 +
   1.359 +
   1.360 +Goal "i: I ==> Applyall {f. (ALL i:I. f i : R) & f i : A} i = R Int A";
   1.361 +by (force_tac (claset(), simpset() addsimps [Applyall_def]) 1);
   1.362 +qed "Applyall_Int";
   1.363 +
   1.364 +
   1.365 +Goal "[| i: I;  finite I |]  \
   1.366 +\     ==> (PPROD I F : Constrains {f. f i : A} {f. f i : B}) =  \
   1.367 +\         (F : Constrains A B)";
   1.368 +by (auto_tac
   1.369 +    (claset(),
   1.370 +     simpset() addsimps [Constrains_def, Collect_conj_eq RS sym,
   1.371 +			 reachable_PPROD_eq]));
   1.372 +bd PPROD_constrains_projection 1;
   1.373 +ba 1;
   1.374 +by (asm_full_simp_tac (simpset() addsimps [Applyall_Int]) 1);
   1.375 +by (auto_tac (claset(), 
   1.376 +              simpset() addsimps [constrains_def, lift_prog_def, PPROD_def,
   1.377 +                                  Acts_JN]));
   1.378 +by (REPEAT (blast_tac (claset() addIs reachable.intrs) 1));
   1.379 +qed "PPROD_Constrains";
   1.380 +
   1.381 +
   1.382 +Goal "[| i: I;  finite I |]  \
   1.383 +\     ==> (PPROD I F : Stable {f. f i : A}) = (F : Stable A)";
   1.384 +by (asm_simp_tac (simpset() addsimps [Stable_def, PPROD_Constrains]) 1);
   1.385 +qed "PPROD_Stable";
   1.386 +
   1.387 +
   1.388 +
     2.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     2.2 +++ b/src/HOL/UNITY/PPROD.thy	Mon Nov 16 13:58:56 1998 +0100
     2.3 @@ -0,0 +1,45 @@
     2.4 +(*  Title:      HOL/UNITY/PPROD.thy
     2.5 +    ID:         $Id$
     2.6 +    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     2.7 +    Copyright   1998  University of Cambridge
     2.8 +
     2.9 +General products of programs (Pi operation).
    2.10 +Also merging of state sets.
    2.11 +*)
    2.12 +
    2.13 +PPROD = Union +
    2.14 +
    2.15 +constdefs
    2.16 +  (*Cartesian product of two relations*)
    2.17 +  RTimes :: "[('a*'a) set, ('b*'b) set] => (('a*'b) * ('a*'b)) set"
    2.18 +	("_ RTimes _" [81, 80] 80)
    2.19 +
    2.20 +    "R RTimes S == {((x,y),(x',y')). (x,x'):R & (y,y'):S}"
    2.21 +
    2.22 +(*FIXME: syntax (symbols) to use <times> ??
    2.23 +  RTimes :: "[('a*'a) set, ('b*'b) set] => (('a*'b) * ('a*'b)) set"
    2.24 +    ("_ \\<times> _" [81, 80] 80)
    2.25 +*)
    2.26 +
    2.27 +constdefs
    2.28 +  Lcopy :: "'a program => ('a*'b) program"
    2.29 +    "Lcopy F == mk_program (Init F Times UNIV,
    2.30 +			    (%act. act RTimes Id) `` Acts F)"
    2.31 +
    2.32 +  lift_act :: "['a, ('b*'b) set] => (('a=>'b) * ('a=>'b)) set"
    2.33 +    "lift_act i act == {(f,f'). EX s'. f' = f(i:=s') & (f i, s') : act}"
    2.34 +
    2.35 +  lift_prog :: "['a, 'b program] => ('a => 'b) program"
    2.36 +    "lift_prog i F == mk_program ({f. f i : Init F}, lift_act i `` Acts F)"
    2.37 +
    2.38 +  (*products of programs*)
    2.39 +  PPROD  :: ['a set, 'b program] => ('a => 'b) program
    2.40 +    "PPROD I F == JN i:I. lift_prog i F"
    2.41 +
    2.42 +syntax
    2.43 +  "@PPROD" :: [pttrn, 'a set, 'b set] => ('a => 'b) set ("(3PPI _:_./ _)" 10)
    2.44 +
    2.45 +translations
    2.46 +  "PPI x:A. B"   == "PPROD A (%x. B)"
    2.47 +
    2.48 +end
     3.1 --- a/src/HOL/UNITY/ROOT.ML	Mon Nov 16 13:58:48 1998 +0100
     3.2 +++ b/src/HOL/UNITY/ROOT.ML	Mon Nov 16 13:58:56 1998 +0100
     3.3 @@ -27,6 +27,7 @@
     3.4  time_use_thy "Lift";
     3.5  time_use_thy "Comp";
     3.6  time_use_thy "Client";
     3.7 +time_use_thy "PPROD";
     3.8  
     3.9  loadpath := "../Auth" :: !loadpath;  (*to find Public.thy*)
    3.10  use_thy"NSP_Bad";