Built-in axioms and theorems
of the
Theorem:
(defthm fn-equal-implies-equal-do$-4 (implies (fn-equal finally-fn finally-fn-equiv) (equal (do$ measure-fn alist do-fn finally-fn values dolia) (do$ measure-fn alist do-fn finally-fn-equiv values dolia))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-do$-3 (implies (fn-equal do-fn do-fn-equiv) (equal (do$ measure-fn alist do-fn finally-fn values dolia) (do$ measure-fn alist do-fn-equiv finally-fn values dolia))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-do$-1 (implies (fn-equal measure-fn measure-fn-equiv) (equal (do$ measure-fn alist do-fn finally-fn values dolia) (do$ measure-fn-equiv alist do-fn finally-fn values dolia))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-append$+-1 (implies (fn-equal fn fn-equiv) (equal (append$+ fn globals lst) (append$+ fn-equiv globals lst))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-append$+-ac-1 (implies (fn-equal fn fn-equiv) (equal (append$+-ac fn globals lst ac) (append$+-ac fn-equiv globals lst ac))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-append$-1 (implies (fn-equal fn fn-equiv) (equal (append$ fn lst) (append$ fn-equiv lst))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-append$-ac-1 (implies (fn-equal fn fn-equiv) (equal (append$-ac fn lst ac) (append$-ac fn-equiv lst ac))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-collect$+-1 (implies (fn-equal fn fn-equiv) (equal (collect$+ fn globals lst) (collect$+ fn-equiv globals lst))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-collect$+-ac-1 (implies (fn-equal fn fn-equiv) (equal (collect$+-ac fn globals lst ac) (collect$+-ac fn-equiv globals lst ac))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-collect$-1 (implies (fn-equal fn fn-equiv) (equal (collect$ fn lst) (collect$ fn-equiv lst))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-collect$-ac-1 (implies (fn-equal fn fn-equiv) (equal (collect$-ac fn lst ac) (collect$-ac fn-equiv lst ac))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-thereis$+-1 (implies (fn-equal fn fn-equiv) (equal (thereis$+ fn globals lst) (thereis$+ fn-equiv globals lst))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-thereis$-1 (implies (fn-equal fn fn-equiv) (equal (thereis$ fn lst) (thereis$ fn-equiv lst))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-always$+-1 (implies (fn-equal fn fn-equiv) (equal (always$+ fn globals lst) (always$+ fn-equiv globals lst))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-always$-1 (implies (fn-equal fn fn-equiv) (equal (always$ fn lst) (always$ fn-equiv lst))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-sum$+-1 (implies (fn-equal fn fn-equiv) (equal (sum$+ fn globals lst) (sum$+ fn-equiv globals lst))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-sum$+-ac-1 (implies (fn-equal fn fn-equiv) (equal (sum$+-ac fn globals lst ac) (sum$+-ac fn-equiv globals lst ac))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-sum$-1 (implies (fn-equal fn fn-equiv) (equal (sum$ fn lst) (sum$ fn-equiv lst))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-sum$-ac-1 (implies (fn-equal fn fn-equiv) (equal (sum$-ac fn lst ac) (sum$-ac fn-equiv lst ac))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-when$+-1 (implies (fn-equal fn fn-equiv) (equal (when$+ fn globals lst) (when$+ fn-equiv globals lst))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-when$+-ac-1 (implies (fn-equal fn fn-equiv) (equal (when$+-ac fn globals lst ac) (when$+-ac fn-equiv globals lst ac))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-when$-1 (implies (fn-equal fn fn-equiv) (equal (when$ fn lst) (when$ fn-equiv lst))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-when$-ac-1 (implies (fn-equal fn fn-equiv) (equal (when$-ac fn lst ac) (when$-ac fn-equiv lst ac))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-until$+-1 (implies (fn-equal fn fn-equiv) (equal (until$+ fn globals lst) (until$+ fn-equiv globals lst))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-until$+-ac-1 (implies (fn-equal fn fn-equiv) (equal (until$+-ac fn globals lst ac) (until$+-ac fn-equiv globals lst ac))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-until$-1 (implies (fn-equal fn fn-equiv) (equal (until$ fn lst) (until$ fn-equiv lst))) :rule-classes (:congruence))
Theorem:
(defthm fn-equal-implies-equal-until$-ac-1 (implies (fn-equal fn fn-equiv) (equal (until$-ac fn lst ac) (until$-ac fn-equiv lst ac))) :rule-classes (:congruence))
Theorem:
(defthm iff-implies-equal-not (implies (iff x x-equiv) (equal (not x) (not x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm iff-implies-equal-implies-2 (implies (iff y y-equiv) (equal (implies x y) (implies x y-equiv))) :rule-classes (:congruence))
Theorem:
(defthm iff-implies-equal-implies-1 (implies (iff x x-equiv) (equal (implies x y) (implies x-equiv y))) :rule-classes (:congruence))