src/ZF/ex/rmap.ML

--- a/src/ZF/ex/rmap.ML	Sat Apr 05 16:18:58 2003 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,82 +0,0 @@
-(*  Title: 	ZF/ex/rmap
-    ID:         $Id$
-    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
-    Copyright   1993  University of Cambridge
-
-Inductive definition of an operator to "map" a relation over a list
-*)
-
-structure Rmap = Inductive_Fun
- (val thy = List.thy addconsts [(["rmap"],"i=>i")];
-  val rec_doms = [("rmap", "list(domain(r))*list(range(r))")];
-  val sintrs = 
-      ["<Nil,Nil> : rmap(r)",
-
-       "[| <x,y>: r;  <xs,ys> : rmap(r) |] ==> \
-\       <Cons(x,xs), Cons(y,ys)> : rmap(r)"];
-  val monos = [];
-  val con_defs = [];
-  val type_intrs = [domainI,rangeI] @ List.intrs @ [SigmaI]
-  val type_elims = [SigmaE2]);
-
-goalw Rmap.thy Rmap.defs "!!r s. r<=s ==> rmap(r) <= rmap(s)";
-by (rtac lfp_mono 1);
-by (REPEAT (rtac Rmap.bnd_mono 1));
-by (REPEAT (ares_tac ([Sigma_mono, list_mono, domain_mono, range_mono] @ 
-		      basic_monos) 1));
-val rmap_mono = result();
-
-val rmap_induct = standard 
-    (Rmap.mutual_induct RS spec RS spec RSN (2,rev_mp));
-
-val Nil_rmap_case = Rmap.mk_cases List.con_defs "<Nil,zs> : rmap(r)"
-and Cons_rmap_case = Rmap.mk_cases List.con_defs "<Cons(x,xs),zs> : rmap(r)";
-
-val rmap_cs = ZF_cs addIs  Rmap.intrs
-		    addSEs [Nil_rmap_case, Cons_rmap_case];
-
-goal Rmap.thy "!!r. r <= A*B ==> rmap(r) <= list(A)*list(B)";
-by (rtac (Rmap.dom_subset RS subset_trans) 1);
-by (REPEAT (ares_tac [domain_rel_subset, range_rel_subset,
-		      Sigma_mono, list_mono] 1));
-val rmap_rel_type = result();
-
-goal Rmap.thy
-    "!!r. [| ALL x:A. EX y. <x,y>: r;  xs: list(A) |] ==> \
-\         EX y. <xs, y> : rmap(r)";
-by (etac List.induct 1);
-by (ALLGOALS (fast_tac rmap_cs));
-val rmap_total = result();
-
-goal Rmap.thy
-    "!!r. [| ALL x y z. <x,y>: r --> <x,z>: r --> y=z;    \
-\            <xs, ys> : rmap(r) |] ==>                    \
-\          ALL zs. <xs, zs> : rmap(r) --> ys=zs";
-by (etac rmap_induct 1);
-by (ALLGOALS (fast_tac rmap_cs));
-val rmap_functional_lemma = result();
-val rmap_functional = standard (rmap_functional_lemma RS spec RS mp);
-
-(** If f is a function then rmap(f) behaves as expected. **)
-
-goal Rmap.thy "!!f. f: A->B ==> rmap(f): list(A)->list(B)";
-by (etac PiE 1);
-by (rtac PiI 1);
-by (etac rmap_rel_type 1);
-by (rtac (rmap_total RS ex_ex1I) 1);
-by (assume_tac 2);
-by (fast_tac (ZF_cs addSEs [bspec RS ex1E]) 1);
-by (rtac rmap_functional 1);
-by (REPEAT (assume_tac 2));
-by (fast_tac (ZF_cs addSEs [bspec RS ex1_equalsE]) 1);
-val rmap_fun_type = result();
-
-goalw Rmap.thy [apply_def] "rmap(f)`Nil = Nil";
-by (fast_tac (rmap_cs addIs [the_equality]) 1);
-val rmap_Nil = result();
-
-goal Rmap.thy "!!f. [| f: A->B;  x: A;  xs: list(A) |] ==> \
-\                   rmap(f) ` Cons(x,xs) = Cons(f`x, rmap(f)`xs)";
-by (rtac apply_equality 1);
-by (REPEAT (ares_tac ([apply_Pair, rmap_fun_type] @ Rmap.intrs) 1));
-val rmap_Cons = result();