src/ZF/InfDatatype.ML
changeset 488 52f7447d4f1b
child 516 1957113f0d7d
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/ZF/InfDatatype.ML	Wed Jul 27 15:33:42 1994 +0200
@@ -0,0 +1,76 @@
+(*  Title: 	ZF/InfDatatype.ML
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1994  University of Cambridge
+
+Infinite-Branching Datatype Definitions
+*)
+
+val fun_Limit_VfromE = 
+    [apply_funtype, InfCard_csucc RS InfCard_is_Limit] MRS Limit_VfromE
+	|> standard;
+
+goal InfDatatype.thy
+    "!!K. [| f: K -> Vfrom(A,csucc(K));  InfCard(K)	\
+\         |] ==> EX j. f: K -> Vfrom(A,j) & j < csucc(K)";
+by (res_inst_tac [("x", "UN k:K. LEAST i. f`k : Vfrom(A,i)")] exI 1);
+by (resolve_tac [conjI] 1);
+by (resolve_tac [ballI RSN (2,cardinal_UN_Ord_lt_csucc)] 2);
+by (eresolve_tac [fun_Limit_VfromE] 3 THEN REPEAT_SOME assume_tac);
+by (fast_tac (ZF_cs addEs [Least_le RS lt_trans1, ltE]) 2);
+by (resolve_tac [Pi_type] 1);
+by (rename_tac "k" 2);
+by (eresolve_tac [fun_Limit_VfromE] 2 THEN REPEAT_SOME assume_tac);
+by (subgoal_tac "f`k : Vfrom(A, LEAST i. f`k : Vfrom(A,i))" 1);
+by (fast_tac (ZF_cs addEs [LeastI, ltE]) 2);
+by (eresolve_tac [[subset_refl, UN_upper] MRS Vfrom_mono RS subsetD] 1);
+by (assume_tac 1);
+val fun_Vfrom_csucc_lemma = result();
+
+goal InfDatatype.thy
+    "!!K. InfCard(K) ==> K -> Vfrom(A,csucc(K)) <= Vfrom(A,csucc(K))";
+by (safe_tac (ZF_cs addSDs [fun_Vfrom_csucc_lemma]));
+by (resolve_tac [Vfrom RS ssubst] 1);
+by (eresolve_tac [PiE] 1);
+(*This level includes the function, and is below csucc(K)*)
+by (res_inst_tac [("a1", "succ(succ(K Un j))")] (UN_I RS UnI2) 1);
+by (eresolve_tac [subset_trans RS PowI] 2);
+by (safe_tac (ZF_cs addSIs [Pair_in_Vfrom]));
+by (fast_tac (ZF_cs addIs [i_subset_Vfrom RS subsetD]) 2);
+by (eresolve_tac [[subset_refl, Un_upper2] MRS Vfrom_mono RS subsetD] 2);
+by (REPEAT (ares_tac [ltD, InfCard_csucc, InfCard_is_Limit, 
+		      Limit_has_succ, Un_least_lt] 1));
+by (eresolve_tac [InfCard_is_Card RS Card_is_Ord RS lt_csucc] 1);
+by (assume_tac 1);
+val fun_Vfrom_csucc = result();
+
+goal InfDatatype.thy
+    "!!K. [| f: K -> Vfrom(A, csucc(K));  InfCard(K) \
+\         |] ==> f: Vfrom(A,csucc(K))";
+by (REPEAT (ares_tac [fun_Vfrom_csucc RS subsetD] 1));
+val fun_in_Vfrom_csucc = result();
+
+val fun_subset_Vfrom_csucc = 
+	[Pi_mono, fun_Vfrom_csucc] MRS subset_trans |> standard;
+
+goal InfDatatype.thy
+    "!!f. [| f: K -> B;  B <= Vfrom(A,csucc(K));  InfCard(K) \
+\         |] ==> f: Vfrom(A,csucc(K))";
+by (REPEAT (ares_tac [fun_subset_Vfrom_csucc RS subsetD] 1));
+val fun_into_Vfrom_csucc = result();
+
+val Limit_csucc = InfCard_csucc RS InfCard_is_Limit |> standard;
+
+val Pair_in_Vfrom_csucc = Limit_csucc RSN (3, Pair_in_Vfrom_Limit) |> standard;
+val Inl_in_Vfrom_csucc  = Limit_csucc RSN (2, Inl_in_Vfrom_Limit) |> standard;
+val Inr_in_Vfrom_csucc  = Limit_csucc RSN (2, Inr_in_Vfrom_Limit) |> standard;
+val zero_in_Vfrom_csucc = Limit_csucc RS zero_in_Vfrom_Limit |> standard;
+val nat_into_Vfrom_csucc = Limit_csucc RSN (2, nat_into_Vfrom_Limit) 
+			   |> standard;
+
+(*For most K-branching datatypes with domain Vfrom(A, csucc(K)) *)
+val inf_datatype_intrs =  
+    [fun_in_Vfrom_csucc, InfCard_nat, Pair_in_Vfrom_csucc, 
+     Inl_in_Vfrom_csucc, Inr_in_Vfrom_csucc, 
+     zero_in_Vfrom_csucc, A_into_Vfrom, nat_into_Vfrom_csucc] @ datatype_intrs;
+