--- a/src/FOL/FOL.thy Wed Dec 21 17:00:57 2005 +0100
+++ b/src/FOL/FOL.thy Thu Dec 22 00:28:34 2005 +0100
@@ -5,12 +5,12 @@
header {* Classical first-order logic *}
-theory FOL
+theory FOL
imports IFOL
uses ("FOL_lemmas1.ML") ("cladata.ML") ("blastdata.ML") ("simpdata.ML")
("eqrule_FOL_data.ML")
("~~/src/Provers/eqsubst.ML")
-begin
+begin
subsection {* The classical axiom *}
@@ -93,33 +93,32 @@
text {* Proper handling of non-atomic rule statements. *}
constdefs
- induct_forall :: "('a => o) => o"
- "induct_forall(P) == \<forall>x. P(x)"
- induct_implies :: "o => o => o"
- "induct_implies(A, B) == A --> B"
- induct_equal :: "'a => 'a => o"
- "induct_equal(x, y) == x = y"
+ induct_forall where "induct_forall(P) == \<forall>x. P(x)"
+ induct_implies where "induct_implies(A, B) == A \<longrightarrow> B"
+ induct_equal where "induct_equal(x, y) == x = y"
+ induct_conj where "induct_conj(A, B) == A \<and> B"
lemma induct_forall_eq: "(!!x. P(x)) == Trueprop(induct_forall(\<lambda>x. P(x)))"
- by (simp only: atomize_all induct_forall_def)
+ by (unfold atomize_all induct_forall_def)
lemma induct_implies_eq: "(A ==> B) == Trueprop(induct_implies(A, B))"
- by (simp only: atomize_imp induct_implies_def)
+ by (unfold atomize_imp induct_implies_def)
lemma induct_equal_eq: "(x == y) == Trueprop(induct_equal(x, y))"
- by (simp only: atomize_eq induct_equal_def)
+ by (unfold atomize_eq induct_equal_def)
-lemma induct_impliesI: "(A ==> B) ==> induct_implies(A, B)"
- by (simp add: induct_implies_def)
+lemma induct_conj_eq:
+ includes meta_conjunction_syntax
+ shows "(A && B) == Trueprop(induct_conj(A, B))"
+ by (unfold atomize_conj induct_conj_def)
-lemmas induct_atomize = atomize_conj induct_forall_eq induct_implies_eq induct_equal_eq
-lemmas induct_rulify1 [symmetric, standard] = induct_forall_eq induct_implies_eq induct_equal_eq
-lemmas induct_rulify2 = induct_forall_def induct_implies_def induct_equal_def
+lemmas induct_atomize_old = induct_forall_eq induct_implies_eq induct_equal_eq atomize_conj
+lemmas induct_atomize = induct_forall_eq induct_implies_eq induct_equal_eq induct_conj_eq
+lemmas induct_rulify [symmetric, standard] = induct_atomize
+lemmas induct_rulify_fallback =
+ induct_forall_def induct_implies_def induct_equal_def induct_conj_def
-lemma all_conj_eq: "(ALL x. P(x)) & (ALL y. Q(y)) == (ALL x y. P(x) & Q(y))"
- by simp
-
-hide const induct_forall induct_implies induct_equal
+hide const induct_forall induct_implies induct_equal induct_conj
text {* Method setup. *}
@@ -127,15 +126,11 @@
ML {*
structure InductMethod = InductMethodFun
(struct
- val dest_concls = FOLogic.dest_concls;
val cases_default = thm "case_split";
- val local_impI = thm "induct_impliesI";
- val conjI = thm "conjI";
+ val atomize_old = thms "induct_atomize_old";
val atomize = thms "induct_atomize";
- val rulify1 = thms "induct_rulify1";
- val rulify2 = thms "induct_rulify2";
- val localize = [Thm.symmetric (thm "induct_implies_def"),
- Thm.symmetric (thm "atomize_all"), thm "all_conj_eq"];
+ val rulify = thms "induct_rulify";
+ val rulify_fallback = thms "induct_rulify_fallback";
end);
*}
--- a/src/HOL/Extraction.thy Wed Dec 21 17:00:57 2005 +0100
+++ b/src/HOL/Extraction.thy Thu Dec 22 00:28:34 2005 +0100
@@ -49,12 +49,12 @@
*}
lemmas [extraction_expand] =
- atomize_eq atomize_all atomize_imp
+ atomize_eq atomize_all atomize_imp atomize_conj
allE rev_mp conjE Eq_TrueI Eq_FalseI eqTrueI eqTrueE eq_cong2
notE' impE' impE iffE imp_cong simp_thms
- induct_forall_eq induct_implies_eq induct_equal_eq
- induct_forall_def induct_implies_def induct_impliesI
- induct_atomize induct_rulify1 induct_rulify2
+ induct_forall_eq induct_implies_eq induct_equal_eq induct_conj_eq
+ induct_forall_def induct_implies_def induct_equal_def induct_conj_def
+ induct_atomize induct_atomize_old induct_rulify induct_rulify_fallback
datatype sumbool = Left | Right
--- a/src/HOL/Inductive.thy Wed Dec 21 17:00:57 2005 +0100
+++ b/src/HOL/Inductive.thy Thu Dec 22 00:28:34 2005 +0100
@@ -67,7 +67,7 @@
imp_conv_disj not_not de_Morgan_disj de_Morgan_conj
not_all not_ex
Ball_def Bex_def
- induct_rulify2
+ induct_rulify_fallback
subsection {* Inductive datatypes and primitive recursion *}