--- a/src/HOL/Option.ML Tue Nov 04 20:47:38 1997 +0100
+++ b/src/HOL/Option.ML Tue Nov 04 20:48:38 1997 +0100
@@ -5,3 +5,55 @@
Derived rules
*)
+open Option;
+
+qed_goal "not_None_eq" thy "(x ~= None) = (? y. x = Some y)"
+ (K [option.induct_tac "x" 1, Auto_tac()]);
+
+section "case analysis in premises";
+
+val optionE = prove_goal thy
+ "[| opt = None ==> P; !!x. opt = Some x ==> P |] ==> P" (fn prems => [
+ case_tac "opt = None" 1,
+ eresolve_tac prems 1,
+ dtac (not_None_eq RS iffD1) 1,
+ etac exE 1,
+ eresolve_tac prems 1]);
+fun optionE_tac s i = EVERY [
+ res_inst_tac [("opt",s)] optionE i,
+ hyp_subst_tac (i+1),
+ hyp_subst_tac i];
+
+qed_goal "option_caseE" thy "[|case x of None => P | Some y => Q y; \
+\ [|x = None; P |] ==> R; \
+\ !!y. [|x = Some y; Q y|] ==> R|] ==> R" (fn prems => [
+ cut_facts_tac prems 1,
+ res_inst_tac [("opt","x")] optionE 1,
+ forward_tac prems 1,
+ forward_tac prems 3,
+ Auto_tac()]);
+fun option_case_tac i = EVERY [
+ etac option_caseE i,
+ hyp_subst_tac (i+1),
+ hyp_subst_tac i];
+
+
+section "the";
+
+qed_goalw "the_Some" thy [the_def]
+ "the (Some x) = x" (K [Simp_tac 1]);
+Addsimps [the_Some];
+
+
+section "option_map";
+
+qed_goalw "option_map_None" thy [option_map_def]
+ "option_map f None = None" (K [Simp_tac 1]);
+qed_goalw "option_map_Some" thy [option_map_def]
+ "option_map f (Some x) = Some (f x)" (K [Simp_tac 1]);
+Addsimps [option_map_None, option_map_Some];
+
+val option_map_SomeD = prove_goalw thy [option_map_def]
+ "!!x. option_map f x = Some y ==> ? z. x = Some z & f z = y" (K [
+ optionE_tac "x" 1,
+ Auto_tac()]);