Built-in axioms and theorems
of the
Theorem:
(defthm dfp-implies-rationalp (implies (dfp x) (rationalp x)) :rule-classes :compound-recognizer)
Theorem:
(defthm bad-atom-compound-recognizer (iff (bad-atom x) (not (or (consp x) (acl2-numberp x) (symbolp x) (characterp x) (stringp x)))) :rule-classes :compound-recognizer)
Theorem:
(defthm posp-compound-recognizer (equal (posp x) (and (integerp x) (< 0 x))) :rule-classes :compound-recognizer)
Theorem:
(defthm bitp-compound-recognizer (equal (bitp x) (or (equal x 0) (equal x 1))) :rule-classes :compound-recognizer)
Theorem:
(defthm natp-compound-recognizer (equal (natp x) (and (integerp x) (<= 0 x))) :rule-classes :compound-recognizer)
Theorem:
(defthm zip-compound-recognizer (equal (zip x) (or (not (integerp x)) (equal x 0))) :rule-classes :compound-recognizer)
Theorem:
(defthm zp-compound-recognizer (equal (zp x) (or (not (integerp x)) (<= x 0))) :rule-classes :compound-recognizer)
Theorem:
(defthm eqlablep-recog (equal (eqlablep x) (or (acl2-numberp x) (symbolp x) (characterp x))) :rule-classes :compound-recognizer)
Theorem:
(defthm booleanp-compound-recognizer (equal (booleanp x) (or (equal x t) (equal x nil))) :rule-classes :compound-recognizer)