Built-in axioms and theorems
of the
Definition:
(defaxiom char-code-linear (< (char-code x) 256) :rule-classes :linear)
Theorem:
(defthm to-df-monotonicity (implies (and (<= x y) (rationalp x) (rationalp y)) (<= (to-df x) (to-df y))) :rule-classes (:linear :rewrite))
Theorem:
(defthm fn-count-evg-rec-bound (< (fn-count-evg-rec evg acc calls) 536870912) :rule-classes :linear)
Theorem:
(defthm acl2-count-car-cdr-linear (implies (consp x) (equal (acl2-count x) (+ 1 (acl2-count (car x)) (acl2-count (cdr x))))) :rule-classes :linear)
Theorem:
(defthm random$-linear (and (<= 0 (car (random$ n state))) (implies (posp n) (< (car (random$ n state)) n))) :rule-classes :linear)
Theorem:
(defthm array2p-linear (implies (array2p name l) (and (< 0 (car (cadr (assoc-keyword :dimensions (cdr (assoc-eq :header l)))))) (< 0 (cadr (cadr (assoc-keyword :dimensions (cdr (assoc-eq :header l)))))) (< (* (car (cadr (assoc-keyword :dimensions (cdr (assoc-eq :header l))))) (cadr (cadr (assoc-keyword :dimensions (cdr (assoc-eq :header l)))))) (cadr (assoc-keyword :maximum-length (cdr (assoc-eq :header l))))) (<= (cadr (assoc-keyword :maximum-length (cdr (assoc-eq :header l)))) (array-maximum-length-bound)))) :rule-classes ((:linear :match-free :all)))
Theorem:
(defthm array1p-linear (implies (array1p name l) (and (< 0 (car (cadr (assoc-keyword :dimensions (cdr (assoc-eq :header l)))))) (< (car (cadr (assoc-keyword :dimensions (cdr (assoc-eq :header l))))) (cadr (assoc-keyword :maximum-length (cdr (assoc-eq :header l))))) (<= (cadr (assoc-keyword :maximum-length (cdr (assoc-eq :header l)))) (array-maximum-length-bound)))) :rule-classes ((:linear :match-free :all)))
Theorem:
(defthm df-round-monotonicity (implies (and (<= x y) (rationalp x) (rationalp y)) (<= (df-round x) (df-round y))) :rule-classes (:linear :rewrite))
Theorem:
(defthm constrained-to-df-monotonicity (implies (and (<= x y) (rationalp x) (rationalp y)) (<= (constrained-to-df x) (constrained-to-df y))) :rule-classes (:linear :rewrite))