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+
+(in-package "BAG")
+
+(include-book "two-level")
+
+;meta rules about bags of bags (the fucntions defined in two-level.lisp)
+;eventually, this books should have its own evaluator.
+
+;;
+;; any-subbagp meta rule ..
+;;
+
+#|
+(defevaluator syntax-ev2 syntax-ev2-list
+ (
+ (hide x)
+ (hide-unique list)
+ (perm x y)
+ (unique list)
+ (implies-if a term)
+ (if a b c)
+ (consp x)
+ (true-listp x)
+ (binary-append x y)
+ (cons a b)
+ (meta-subbagp list1 list2)
+ (remove-bag x list)
+ (meta-remove-bag x list)
+ (remove-1 x list)
+ (meta-remove-1 x list)
+ (unique-subbagps x y list)
+ (subbagp-pair x1 x2 list1 list2)
+ (meta-memberp x list)
+ (any-subbagp x list)
+ ))
+|#
+
+#|
+(encapsulate
+ ()
+
+ (local
+ (defthm syntax-subbagp-implements-subbagp-syntax-ev2-nil
+ (implies
+ (and
+ (v0 (syntax-remove-bag list1 list2 flg))
+ (equal (syntax-ev2 (v2 (syntax-remove-bag list1 list2 flg)) a)
+ nil)
+ )
+ (subbagp (syntax-ev2 list2 a) (syntax-ev2 list1 a))))
+ )
+
+(DEFTHM SYNTAX-SUBBAGP-IMPLEMENTS-SUBBAGP-2
+ (IMPLIES (AND (V0 (SYNTAX-REMOVE-BAG LIST1 LIST2 FLG))
+ (EQUAL (V2 (SYNTAX-REMOVE-BAG LIST1 LIST2 FLG))
+ ''NIL))
+ (SUBBAGP (SYNTAX-EV2 LIST2 A)
+ (SYNTAX-EV2 LIST1 A))))
+ )
+|#
+
+
+(defun syntax-deconsp (list)
+ (declare (type t list))
+ (if (and (consp list)
+ (equal (car list) 'cons)
+ (consp (cdr list))
+ (consp (cddr list))
+ (null (cdddr list)))
+ (mv t (cadr list) (caddr list))
+ (mv nil nil nil)))
+
+(defignored syntax-subbagp-list a (x list)
+ (declare (type t x list)
+ (xargs :guard (and (pseudo-termp x)
+ (pseudo-termp list)
+ )
+ )
+ )
+ (met ((consp entry rst) (syntax-deconsp list))
+ (if consp
+ (if (syntax-subbagp x entry) t
+ (syntax-subbagp-list x rst))
+ nil)))
+
+(defirrelevant syntax-subbagp-list 1 a (x list)
+ :hints (("goal" :in-theory (enable
+ syntax-subbagp-list
+ syntax-subbagp-irrelevant
+ ))))
+
+(defun syntax-subbagp-list-wrapper (term)
+ (declare (type t term)
+ (xargs :guard (pseudo-termp term)
+ ))
+ (if (and (consp term)
+ (equal (car term) 'any-subbagp)
+ (consp (cdr term))
+ (consp (cddr term))
+ (null (cdddr term))
+ (syntax-subbagp-list-fn nil (cadr term) (caddr term)))
+ '(quote t)
+ term))
+
+(defthm syntax-subbagp-implies-any-subbagp
+ (implies (syntax-subbagp-list term1 term2)
+ (any-subbagp (syntax-ev term1 a) (syntax-ev term2 a)))
+ :rule-classes (:rewrite :forward-chaining)
+ :hints (("Goal" :in-theory (enable syntax-subbagp-list any-subbagp))))
+
+(defthm *meta*-subbagp-list
+ (equal (syntax-ev term a)
+ (syntax-ev (syntax-subbagp-list-wrapper term) a))
+ :hints (("goal" :in-theory (enable syntax-subbagp-list-irrelevant)))
+ :rule-classes ((:meta :trigger-fns (any-subbagp))))