src/Pure/drule.ML
changeset 0 a5a9c433f639
child 11 d0e17c42dbb4
equal deleted inserted replaced
-1:000000000000 0:a5a9c433f639
       
     1 (*  Title: 	drule
       
     2     ID:         $Id$
       
     3     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
       
     4     Copyright   1993  University of Cambridge
       
     5 
       
     6 Derived rules and other operations on theorems and theories
       
     7 *)
       
     8 
       
     9 infix 0 RS RSN RL RLN COMP;
       
    10 
       
    11 signature DRULE =
       
    12   sig
       
    13   structure Thm : THM
       
    14   local open Thm  in
       
    15   val asm_rl: thm
       
    16   val assume_ax: theory -> string -> thm
       
    17   val COMP: thm * thm -> thm
       
    18   val compose: thm * int * thm -> thm list
       
    19   val cterm_instantiate: (Sign.cterm*Sign.cterm)list -> thm -> thm
       
    20   val cut_rl: thm
       
    21   val equal_abs_elim: Sign.cterm  -> thm -> thm
       
    22   val equal_abs_elim_list: Sign.cterm list -> thm -> thm
       
    23   val eq_sg: Sign.sg * Sign.sg -> bool
       
    24   val eq_thm: thm * thm -> bool
       
    25   val eq_thm_sg: thm * thm -> bool
       
    26   val flexpair_abs_elim_list: Sign.cterm list -> thm -> thm
       
    27   val forall_intr_list: Sign.cterm list -> thm -> thm
       
    28   val forall_intr_frees: thm -> thm
       
    29   val forall_elim_list: Sign.cterm list -> thm -> thm
       
    30   val forall_elim_var: int -> thm -> thm
       
    31   val forall_elim_vars: int -> thm -> thm
       
    32   val implies_elim_list: thm -> thm list -> thm
       
    33   val implies_intr_list: Sign.cterm list -> thm -> thm
       
    34   val print_cterm: Sign.cterm -> unit
       
    35   val print_ctyp: Sign.ctyp -> unit
       
    36   val print_goals: int -> thm -> unit
       
    37   val print_sg: Sign.sg -> unit
       
    38   val print_theory: theory -> unit
       
    39   val pprint_sg: Sign.sg -> pprint_args -> unit
       
    40   val pprint_theory: theory -> pprint_args -> unit
       
    41   val print_thm: thm -> unit
       
    42   val prth: thm -> thm
       
    43   val prthq: thm Sequence.seq -> thm Sequence.seq
       
    44   val prths: thm list -> thm list
       
    45   val read_instantiate: (string*string)list -> thm -> thm
       
    46   val read_instantiate_sg: Sign.sg -> (string*string)list -> thm -> thm
       
    47   val reflexive_thm: thm
       
    48   val revcut_rl: thm
       
    49   val rewrite_goal_rule: (meta_simpset -> thm -> thm option) -> meta_simpset ->
       
    50         int -> thm -> thm
       
    51   val rewrite_goals_rule: thm list -> thm -> thm
       
    52   val rewrite_rule: thm list -> thm -> thm
       
    53   val RS: thm * thm -> thm
       
    54   val RSN: thm * (int * thm) -> thm
       
    55   val RL: thm list * thm list -> thm list
       
    56   val RLN: thm list * (int * thm list) -> thm list
       
    57   val show_hyps: bool ref
       
    58   val size_of_thm: thm -> int
       
    59   val standard: thm -> thm
       
    60   val string_of_thm: thm -> string
       
    61   val symmetric_thm: thm
       
    62   val pprint_thm: thm -> pprint_args -> unit
       
    63   val transitive_thm: thm
       
    64   val triv_forall_equality: thm
       
    65   val types_sorts: thm -> (indexname-> typ option) * (indexname-> sort option)
       
    66   val zero_var_indexes: thm -> thm
       
    67   end
       
    68   end;
       
    69 
       
    70 functor DruleFun (structure Logic: LOGIC and Thm: THM) : DRULE = 
       
    71 struct
       
    72 structure Thm = Thm;
       
    73 structure Sign = Thm.Sign;
       
    74 structure Type = Sign.Type;
       
    75 structure Pretty = Sign.Syntax.Pretty
       
    76 local open Thm
       
    77 in
       
    78 
       
    79 (**** More derived rules and operations on theorems ****)
       
    80 
       
    81 (*** Find the type (sort) associated with a (T)Var or (T)Free in a term 
       
    82      Used for establishing default types (of variables) and sorts (of
       
    83      type variables) when reading another term.
       
    84      Index -1 indicates that a (T)Free rather than a (T)Var is wanted.
       
    85 ***)
       
    86 
       
    87 fun types_sorts thm =
       
    88     let val {prop,hyps,...} = rep_thm thm;
       
    89 	val big = list_comb(prop,hyps); (* bogus term! *)
       
    90 	val vars = map dest_Var (term_vars big);
       
    91 	val frees = map dest_Free (term_frees big);
       
    92 	val tvars = term_tvars big;
       
    93 	val tfrees = term_tfrees big;
       
    94 	fun typ(a,i) = if i<0 then assoc(frees,a) else assoc(vars,(a,i));
       
    95 	fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i));
       
    96     in (typ,sort) end;
       
    97 
       
    98 (** Standardization of rules **)
       
    99 
       
   100 (*Generalization over a list of variables, IGNORING bad ones*)
       
   101 fun forall_intr_list [] th = th
       
   102   | forall_intr_list (y::ys) th =
       
   103 	let val gth = forall_intr_list ys th
       
   104 	in  forall_intr y gth   handle THM _ =>  gth  end;
       
   105 
       
   106 (*Generalization over all suitable Free variables*)
       
   107 fun forall_intr_frees th =
       
   108     let val {prop,sign,...} = rep_thm th
       
   109     in  forall_intr_list
       
   110          (map (Sign.cterm_of sign) (sort atless (term_frees prop))) 
       
   111          th
       
   112     end;
       
   113 
       
   114 (*Replace outermost quantified variable by Var of given index.
       
   115     Could clash with Vars already present.*)
       
   116 fun forall_elim_var i th = 
       
   117     let val {prop,sign,...} = rep_thm th
       
   118     in case prop of
       
   119 	  Const("all",_) $ Abs(a,T,_) =>
       
   120 	      forall_elim (Sign.cterm_of sign (Var((a,i), T)))  th
       
   121 	| _ => raise THM("forall_elim_var", i, [th])
       
   122     end;
       
   123 
       
   124 (*Repeat forall_elim_var until all outer quantifiers are removed*)
       
   125 fun forall_elim_vars i th = 
       
   126     forall_elim_vars i (forall_elim_var i th)
       
   127 	handle THM _ => th;
       
   128 
       
   129 (*Specialization over a list of cterms*)
       
   130 fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th);
       
   131 
       
   132 (* maps [A1,...,An], B   to   [| A1;...;An |] ==> B  *)
       
   133 fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th);
       
   134 
       
   135 (* maps [| A1;...;An |] ==> B and [A1,...,An]   to   B *)
       
   136 fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths);
       
   137 
       
   138 (*Reset Var indexes to zero, renaming to preserve distinctness*)
       
   139 fun zero_var_indexes th = 
       
   140     let val {prop,sign,...} = rep_thm th;
       
   141         val vars = term_vars prop
       
   142         val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars)
       
   143 	val inrs = add_term_tvars(prop,[]);
       
   144 	val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs));
       
   145 	val tye = map (fn ((v,rs),a) => (v, TVar((a,0),rs))) (inrs ~~ nms')
       
   146 	val ctye = map (fn (v,T) => (v,Sign.ctyp_of sign T)) tye;
       
   147 	fun varpairs([],[]) = []
       
   148 	  | varpairs((var as Var(v,T)) :: vars, b::bs) =
       
   149 		let val T' = typ_subst_TVars tye T
       
   150 		in (Sign.cterm_of sign (Var(v,T')),
       
   151 		    Sign.cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs)
       
   152 		end
       
   153 	  | varpairs _ = raise TERM("varpairs", []);
       
   154     in instantiate (ctye, varpairs(vars,rev bs)) th end;
       
   155 
       
   156 
       
   157 (*Standard form of object-rule: no hypotheses, Frees, or outer quantifiers;
       
   158     all generality expressed by Vars having index 0.*)
       
   159 fun standard th =
       
   160     let val {maxidx,...} = rep_thm th
       
   161     in  varifyT (zero_var_indexes (forall_elim_vars(maxidx+1) 
       
   162                          (forall_intr_frees(implies_intr_hyps th))))
       
   163     end;
       
   164 
       
   165 (*Assume a new formula, read following the same conventions as axioms. 
       
   166   Generalizes over Free variables,
       
   167   creates the assumption, and then strips quantifiers.
       
   168   Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
       
   169 	     [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
       
   170 fun assume_ax thy sP =
       
   171     let val sign = sign_of thy
       
   172 	val prop = Logic.close_form (Sign.term_of (Sign.read_cterm sign
       
   173 			 (sP, propT)))
       
   174     in forall_elim_vars 0 (assume (Sign.cterm_of sign prop))  end;
       
   175 
       
   176 (*Resolution: exactly one resolvent must be produced.*) 
       
   177 fun tha RSN (i,thb) =
       
   178   case Sequence.chop (2, biresolution false [(false,tha)] i thb) of
       
   179       ([th],_) => th
       
   180     | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
       
   181     |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
       
   182 
       
   183 (*resolution: P==>Q, Q==>R gives P==>R. *)
       
   184 fun tha RS thb = tha RSN (1,thb);
       
   185 
       
   186 (*For joining lists of rules*)
       
   187 fun thas RLN (i,thbs) = 
       
   188   let val resolve = biresolution false (map (pair false) thas) i
       
   189       fun resb thb = Sequence.list_of_s (resolve thb) handle THM _ => []
       
   190   in  flat (map resb thbs)  end;
       
   191 
       
   192 fun thas RL thbs = thas RLN (1,thbs);
       
   193 
       
   194 (*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R 
       
   195   with no lifting or renaming!  Q may contain ==> or meta-quants
       
   196   ALWAYS deletes premise i *)
       
   197 fun compose(tha,i,thb) = 
       
   198     Sequence.list_of_s (bicompose false (false,tha,0) i thb);
       
   199 
       
   200 (*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
       
   201 fun tha COMP thb =
       
   202     case compose(tha,1,thb) of
       
   203         [th] => th  
       
   204       | _ =>   raise THM("COMP", 1, [tha,thb]);
       
   205 
       
   206 (*Instantiate theorem th, reading instantiations under signature sg*)
       
   207 fun read_instantiate_sg sg sinsts th =
       
   208     let val ts = types_sorts th;
       
   209         val instpair = Sign.read_insts sg ts ts sinsts
       
   210     in  instantiate instpair th  end;
       
   211 
       
   212 (*Instantiate theorem th, reading instantiations under theory of th*)
       
   213 fun read_instantiate sinsts th =
       
   214     read_instantiate_sg (#sign (rep_thm th)) sinsts th;
       
   215 
       
   216 
       
   217 (*Left-to-right replacements: tpairs = [...,(vi,ti),...].
       
   218   Instantiates distinct Vars by terms, inferring type instantiations. *)
       
   219 local
       
   220   fun add_types ((ct,cu), (sign,tye)) =
       
   221     let val {sign=signt, t=t, T= T, ...} = Sign.rep_cterm ct
       
   222         and {sign=signu, t=u, T= U, ...} = Sign.rep_cterm cu
       
   223         val sign' = Sign.merge(sign, Sign.merge(signt, signu))
       
   224 	val tye' = Type.unify (#tsig(Sign.rep_sg sign')) ((T,U), tye)
       
   225 	  handle Type.TUNIFY => raise TYPE("add_types", [T,U], [t,u])
       
   226     in  (sign', tye')  end;
       
   227 in
       
   228 fun cterm_instantiate ctpairs0 th = 
       
   229   let val (sign,tye) = foldr add_types (ctpairs0, (#sign(rep_thm th),[]))
       
   230       val tsig = #tsig(Sign.rep_sg sign);
       
   231       fun instT(ct,cu) = let val inst = subst_TVars tye
       
   232 			 in (Sign.cfun inst ct, Sign.cfun inst cu) end
       
   233       fun ctyp2 (ix,T) = (ix, Sign.ctyp_of sign T)
       
   234   in  instantiate (map ctyp2 tye, map instT ctpairs0) th  end
       
   235   handle TERM _ => 
       
   236            raise THM("cterm_instantiate: incompatible signatures",0,[th])
       
   237        | TYPE _ => raise THM("cterm_instantiate: types", 0, [th])
       
   238 end;
       
   239 
       
   240 
       
   241 (*** Printing of theorems ***)
       
   242 
       
   243 (*If false, hypotheses are printed as dots*)
       
   244 val show_hyps = ref true;
       
   245 
       
   246 fun pretty_thm th =
       
   247 let val {sign, hyps, prop,...} = rep_thm th
       
   248     val hsymbs = if null hyps then []
       
   249 		 else if !show_hyps then
       
   250 		      [Pretty.brk 2,
       
   251 		       Pretty.lst("[","]") (map (Sign.pretty_term sign) hyps)]
       
   252 		 else Pretty.str" [" :: map (fn _ => Pretty.str".") hyps @
       
   253 		      [Pretty.str"]"];
       
   254 in Pretty.blk(0, Sign.pretty_term sign prop :: hsymbs) end;
       
   255 
       
   256 val string_of_thm = Pretty.string_of o pretty_thm;
       
   257 
       
   258 val pprint_thm = Pretty.pprint o Pretty.quote o pretty_thm;
       
   259 
       
   260 
       
   261 (** Top-level commands for printing theorems **)
       
   262 val print_thm = writeln o string_of_thm;
       
   263 
       
   264 fun prth th = (print_thm th; th);
       
   265 
       
   266 (*Print and return a sequence of theorems, separated by blank lines. *)
       
   267 fun prthq thseq =
       
   268     (Sequence.prints (fn _ => print_thm) 100000 thseq;
       
   269      thseq);
       
   270 
       
   271 (*Print and return a list of theorems, separated by blank lines. *)
       
   272 fun prths ths = (print_list_ln print_thm ths; ths);
       
   273 
       
   274 (*Other printing commands*)
       
   275 val print_cterm = writeln o Sign.string_of_cterm;
       
   276 val print_ctyp = writeln o Sign.string_of_ctyp;
       
   277 fun pretty_sg sg = 
       
   278   Pretty.lst ("{", "}") (map (Pretty.str o !) (#stamps (Sign.rep_sg sg)));
       
   279 
       
   280 val pprint_sg = Pretty.pprint o pretty_sg;
       
   281 
       
   282 val pprint_theory = pprint_sg o sign_of;
       
   283 
       
   284 val print_sg = writeln o Pretty.string_of o pretty_sg;
       
   285 val print_theory = print_sg o sign_of;
       
   286 
       
   287 
       
   288 (** Print thm A1,...,An/B in "goal style" -- premises as numbered subgoals **)
       
   289 
       
   290 fun prettyprints es = writeln(Pretty.string_of(Pretty.blk(0,es)));
       
   291 
       
   292 fun print_goals maxgoals th : unit =
       
   293 let val {sign, hyps, prop,...} = rep_thm th;
       
   294     fun printgoals (_, []) = ()
       
   295       | printgoals (n, A::As) =
       
   296 	let val prettyn = Pretty.str(" " ^ string_of_int n ^ ". ");
       
   297 	    val prettyA = Sign.pretty_term sign A
       
   298 	in prettyprints[prettyn,prettyA]; 
       
   299            printgoals (n+1,As) 
       
   300         end;
       
   301     fun prettypair(t,u) =
       
   302         Pretty.blk(0, [Sign.pretty_term sign t, Pretty.str" =?=", Pretty.brk 1,
       
   303 		       Sign.pretty_term sign u]);
       
   304     fun printff [] = ()
       
   305       | printff tpairs =
       
   306 	 writeln("\nFlex-flex pairs:\n" ^
       
   307 		 Pretty.string_of(Pretty.lst("","") (map prettypair tpairs)))
       
   308     val (tpairs,As,B) = Logic.strip_horn(prop);
       
   309     val ngoals = length As
       
   310 in 
       
   311    writeln (Sign.string_of_term sign B);
       
   312    if ngoals=0 then writeln"No subgoals!"
       
   313    else if ngoals>maxgoals 
       
   314         then (printgoals (1, take(maxgoals,As));
       
   315 	      writeln("A total of " ^ string_of_int ngoals ^ " subgoals..."))
       
   316         else printgoals (1, As);
       
   317    printff tpairs
       
   318 end;
       
   319 
       
   320 
       
   321 (** theorem equality test is exported and used by BEST_FIRST **)
       
   322 
       
   323 (*equality of signatures means exact identity -- by ref equality*)
       
   324 fun eq_sg (sg1,sg2) = (#stamps(Sign.rep_sg sg1) = #stamps(Sign.rep_sg sg2));
       
   325 
       
   326 (*equality of theorems uses equality of signatures and 
       
   327   the a-convertible test for terms*)
       
   328 fun eq_thm (th1,th2) = 
       
   329     let val {sign=sg1, hyps=hyps1, prop=prop1, ...} = rep_thm th1
       
   330 	and {sign=sg2, hyps=hyps2, prop=prop2, ...} = rep_thm th2
       
   331     in  eq_sg (sg1,sg2) andalso 
       
   332         aconvs(hyps1,hyps2) andalso 
       
   333         prop1 aconv prop2  
       
   334     end;
       
   335 
       
   336 (*Do the two theorems have the same signature?*)
       
   337 fun eq_thm_sg (th1,th2) = eq_sg(#sign(rep_thm th1), #sign(rep_thm th2));
       
   338 
       
   339 (*Useful "distance" function for BEST_FIRST*)
       
   340 val size_of_thm = size_of_term o #prop o rep_thm;
       
   341 
       
   342 
       
   343 (*** Meta-Rewriting Rules ***)
       
   344 
       
   345 
       
   346 val reflexive_thm =
       
   347   let val cx = Sign.cterm_of Sign.pure (Var(("x",0),TVar(("'a",0),["logic"])))
       
   348   in Thm.reflexive cx end;
       
   349 
       
   350 val symmetric_thm =
       
   351   let val xy = Sign.read_cterm Sign.pure ("x::'a::logic == y",propT)
       
   352   in standard(Thm.implies_intr_hyps(Thm.symmetric(Thm.assume xy))) end;
       
   353 
       
   354 val transitive_thm =
       
   355   let val xy = Sign.read_cterm Sign.pure ("x::'a::logic == y",propT)
       
   356       val yz = Sign.read_cterm Sign.pure ("y::'a::logic == z",propT)
       
   357       val xythm = Thm.assume xy and yzthm = Thm.assume yz
       
   358   in standard(Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
       
   359 
       
   360 
       
   361 (** Below, a "conversion" has type sign->term->thm **)
       
   362 
       
   363 (*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
       
   364 fun goals_conv pred cv sign = 
       
   365   let val triv = reflexive o Sign.cterm_of sign
       
   366       fun gconv i t =
       
   367         let val (A,B) = Logic.dest_implies t
       
   368 	    val thA = if (pred i) then (cv sign A) else (triv A)
       
   369 	in  combination (combination (triv implies) thA)
       
   370                         (gconv (i+1) B)
       
   371         end
       
   372         handle TERM _ => triv t
       
   373   in gconv 1 end;
       
   374 
       
   375 (*Use a conversion to transform a theorem*)
       
   376 fun fconv_rule cv th =
       
   377   let val {sign,prop,...} = rep_thm th
       
   378   in  equal_elim (cv sign prop) th  end;
       
   379 
       
   380 (*rewriting conversion*)
       
   381 fun rew_conv prover mss sign t =
       
   382   rewrite_cterm mss prover (Sign.cterm_of sign t);
       
   383 
       
   384 (*Rewrite a theorem*)
       
   385 fun rewrite_rule thms = fconv_rule (rew_conv (K(K None)) (Thm.mss_of thms));
       
   386 
       
   387 (*Rewrite the subgoals of a proof state (represented by a theorem) *)
       
   388 fun rewrite_goals_rule thms =
       
   389   fconv_rule (goals_conv (K true) (rew_conv (K(K None)) (Thm.mss_of thms)));
       
   390 
       
   391 (*Rewrite the subgoal of a proof state (represented by a theorem) *)
       
   392 fun rewrite_goal_rule prover mss i =
       
   393       fconv_rule (goals_conv (fn j => j=i) (rew_conv prover mss));
       
   394 
       
   395 
       
   396 (** Derived rules mainly for METAHYPS **)
       
   397 
       
   398 (*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
       
   399 fun equal_abs_elim ca eqth =
       
   400   let val {sign=signa, t=a, ...} = Sign.rep_cterm ca
       
   401       and combth = combination eqth (reflexive ca)
       
   402       val {sign,prop,...} = rep_thm eqth
       
   403       val (abst,absu) = Logic.dest_equals prop
       
   404       val cterm = Sign.cterm_of (Sign.merge (sign,signa))
       
   405   in  transitive (symmetric (beta_conversion (cterm (abst$a))))
       
   406            (transitive combth (beta_conversion (cterm (absu$a))))
       
   407   end
       
   408   handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
       
   409 
       
   410 (*Calling equal_abs_elim with multiple terms*)
       
   411 fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th);
       
   412 
       
   413 local
       
   414   open Logic
       
   415   val alpha = TVar(("'a",0), [])     (*  type ?'a::{}  *)
       
   416   fun err th = raise THM("flexpair_inst: ", 0, [th])
       
   417   fun flexpair_inst def th =
       
   418     let val {prop = Const _ $ t $ u,  sign,...} = rep_thm th
       
   419 	val cterm = Sign.cterm_of sign
       
   420 	fun cvar a = cterm(Var((a,0),alpha))
       
   421 	val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)] 
       
   422 		   def
       
   423     in  equal_elim def' th
       
   424     end
       
   425     handle THM _ => err th | bind => err th
       
   426 in
       
   427 val flexpair_intr = flexpair_inst (symmetric flexpair_def)
       
   428 and flexpair_elim = flexpair_inst flexpair_def
       
   429 end;
       
   430 
       
   431 (*Version for flexflex pairs -- this supports lifting.*)
       
   432 fun flexpair_abs_elim_list cts = 
       
   433     flexpair_intr o equal_abs_elim_list cts o flexpair_elim;
       
   434 
       
   435 
       
   436 (*** Some useful meta-theorems ***)
       
   437 
       
   438 (*The rule V/V, obtains assumption solving for eresolve_tac*)
       
   439 val asm_rl = trivial(Sign.read_cterm Sign.pure ("PROP ?psi",propT));
       
   440 
       
   441 (*Meta-level cut rule: [| V==>W; V |] ==> W *)
       
   442 val cut_rl = trivial(Sign.read_cterm Sign.pure 
       
   443 	("PROP ?psi ==> PROP ?theta", propT));
       
   444 
       
   445 (*Generalized elim rule for one conclusion; cut_rl with reversed premises: 
       
   446      [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
       
   447 val revcut_rl =
       
   448   let val V = Sign.read_cterm Sign.pure ("PROP V", propT)
       
   449       and VW = Sign.read_cterm Sign.pure ("PROP V ==> PROP W", propT);
       
   450   in  standard (implies_intr V 
       
   451 		(implies_intr VW
       
   452 		 (implies_elim (assume VW) (assume V))))
       
   453   end;
       
   454 
       
   455 (* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
       
   456 val triv_forall_equality =
       
   457   let val V  = Sign.read_cterm Sign.pure ("PROP V", propT)
       
   458       and QV = Sign.read_cterm Sign.pure ("!!x::'a. PROP V", propT)
       
   459       and x  = Sign.read_cterm Sign.pure ("x", TFree("'a",["logic"]));
       
   460   in  standard (equal_intr (implies_intr QV (forall_elim x (assume QV)))
       
   461 		           (implies_intr V  (forall_intr x (assume V))))
       
   462   end;
       
   463 
       
   464 end
       
   465 end;