Built-in axioms and theorems
of the
Theorem:
(defthm apply$-warrant-do$-definition (equal (apply$-warrant-do$) (let ((args (apply$-warrant-do$-witness))) (implies (and (tamep-functionp (car args)) (tamep-functionp (car (cdr (cdr args)))) (tamep-functionp (car (cdr (cdr (cdr args)))))) (and (equal (badge-userfn 'do$) '(apply$-badge 6 1 :fn nil :fn :fn nil nil)) (equal (apply$-userfn 'do$ args) (do$ (car args) (car (cdr args)) (car (cdr (cdr args))) (car (cdr (cdr (cdr args)))) (car (cdr (cdr (cdr (cdr args))))) (car (cdr (cdr (cdr (cdr (cdr args)))))))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-loop$-default-values-definition (equal (apply$-warrant-loop$-default-values) (let ((args (apply$-warrant-loop$-default-values-witness))) (and (equal (badge-userfn 'loop$-default-values) '(apply$-badge 2 1 . t)) (equal (apply$-userfn 'loop$-default-values args) (loop$-default-values (car args) (car (cdr args))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-loop$-default-values1-definition (equal (apply$-warrant-loop$-default-values1) (let ((args (apply$-warrant-loop$-default-values1-witness))) (and (equal (badge-userfn 'loop$-default-values1) '(apply$-badge 2 1 . t)) (equal (apply$-userfn 'loop$-default-values1 args) (loop$-default-values1 (car args) (car (cdr args))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-eviscerate-do$-alist-definition (equal (apply$-warrant-eviscerate-do$-alist) (let ((args (apply$-warrant-eviscerate-do$-alist-witness))) (and (equal (badge-userfn 'eviscerate-do$-alist) '(apply$-badge 2 1 . t)) (equal (apply$-userfn 'eviscerate-do$-alist args) (eviscerate-do$-alist (car args) (car (cdr args))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-stobj-print-name-definition (equal (apply$-warrant-stobj-print-name) (let ((args (apply$-warrant-stobj-print-name-witness))) (and (equal (badge-userfn 'stobj-print-name) '(apply$-badge 1 1 . t)) (equal (apply$-userfn 'stobj-print-name args) (stobj-print-name (car args)))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-lexp-definition (equal (apply$-warrant-lexp) (let ((args (apply$-warrant-lexp-witness))) (and (equal (badge-userfn 'lexp) '(apply$-badge 1 1 . t)) (equal (apply$-userfn 'lexp args) (lexp (car args)))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-lex-fix-definition (equal (apply$-warrant-lex-fix) (let ((args (apply$-warrant-lex-fix-witness))) (and (equal (badge-userfn 'lex-fix) '(apply$-badge 1 1 . t)) (equal (apply$-userfn 'lex-fix args) (lex-fix (car args)))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-nfix-list-definition (equal (apply$-warrant-nfix-list) (let ((args (apply$-warrant-nfix-list-witness))) (and (equal (badge-userfn 'nfix-list) '(apply$-badge 1 1 . t)) (equal (apply$-userfn 'nfix-list args) (nfix-list (car args)))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-l<-definition (equal (apply$-warrant-l<) (let ((args (apply$-warrant-l<-witness))) (and (equal (badge-userfn 'l<) '(apply$-badge 2 1 . t)) (equal (apply$-userfn 'l< args) (l< (car args) (car (cdr args))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-d<-definition (equal (apply$-warrant-d<) (let ((args (apply$-warrant-d<-witness))) (and (equal (badge-userfn 'd<) '(apply$-badge 2 1 . t)) (equal (apply$-userfn 'd< args) (d< (car args) (car (cdr args))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-mempos-definition (equal (apply$-warrant-mempos) (let ((args (apply$-warrant-mempos-witness))) (and (equal (badge-userfn 'mempos) '(apply$-badge 2 1 . t)) (equal (apply$-userfn 'mempos args) (mempos (car args) (car (cdr args))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-append$+-definition (equal (apply$-warrant-append$+) (let ((args (apply$-warrant-append$+-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'append$+) '(apply$-badge 3 1 :fn nil nil)) (equal (apply$-userfn 'append$+ args) (append$+ (car args) (car (cdr args)) (car (cdr (cdr args))))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-append$+-ac-definition (equal (apply$-warrant-append$+-ac) (let ((args (apply$-warrant-append$+-ac-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'append$+-ac) '(apply$-badge 4 1 :fn nil nil nil)) (equal (apply$-userfn 'append$+-ac args) (append$+-ac (car args) (car (cdr args)) (car (cdr (cdr args))) (car (cdr (cdr (cdr args)))))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-append$-definition (equal (apply$-warrant-append$) (let ((args (apply$-warrant-append$-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'append$) '(apply$-badge 2 1 :fn nil)) (equal (apply$-userfn 'append$ args) (append$ (car args) (car (cdr args)))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-append$-ac-definition (equal (apply$-warrant-append$-ac) (let ((args (apply$-warrant-append$-ac-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'append$-ac) '(apply$-badge 3 1 :fn nil nil)) (equal (apply$-userfn 'append$-ac args) (append$-ac (car args) (car (cdr args)) (car (cdr (cdr args))))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-collect$+-definition (equal (apply$-warrant-collect$+) (let ((args (apply$-warrant-collect$+-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'collect$+) '(apply$-badge 3 1 :fn nil nil)) (equal (apply$-userfn 'collect$+ args) (collect$+ (car args) (car (cdr args)) (car (cdr (cdr args))))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-collect$+-ac-definition (equal (apply$-warrant-collect$+-ac) (let ((args (apply$-warrant-collect$+-ac-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'collect$+-ac) '(apply$-badge 4 1 :fn nil nil nil)) (equal (apply$-userfn 'collect$+-ac args) (collect$+-ac (car args) (car (cdr args)) (car (cdr (cdr args))) (car (cdr (cdr (cdr args)))))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-collect$-definition (equal (apply$-warrant-collect$) (let ((args (apply$-warrant-collect$-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'collect$) '(apply$-badge 2 1 :fn nil)) (equal (apply$-userfn 'collect$ args) (collect$ (car args) (car (cdr args)))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-collect$-ac-definition (equal (apply$-warrant-collect$-ac) (let ((args (apply$-warrant-collect$-ac-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'collect$-ac) '(apply$-badge 3 1 :fn nil nil)) (equal (apply$-userfn 'collect$-ac args) (collect$-ac (car args) (car (cdr args)) (car (cdr (cdr args))))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-thereis$+-definition (equal (apply$-warrant-thereis$+) (let ((args (apply$-warrant-thereis$+-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'thereis$+) '(apply$-badge 3 1 :fn nil nil)) (equal (apply$-userfn 'thereis$+ args) (thereis$+ (car args) (car (cdr args)) (car (cdr (cdr args))))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-thereis$-definition (equal (apply$-warrant-thereis$) (let ((args (apply$-warrant-thereis$-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'thereis$) '(apply$-badge 2 1 :fn nil)) (equal (apply$-userfn 'thereis$ args) (thereis$ (car args) (car (cdr args)))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-always$+-definition (equal (apply$-warrant-always$+) (let ((args (apply$-warrant-always$+-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'always$+) '(apply$-badge 3 1 :fn nil nil)) (equal (apply$-userfn 'always$+ args) (always$+ (car args) (car (cdr args)) (car (cdr (cdr args))))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-always$-definition (equal (apply$-warrant-always$) (let ((args (apply$-warrant-always$-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'always$) '(apply$-badge 2 1 :fn nil)) (equal (apply$-userfn 'always$ args) (always$ (car args) (car (cdr args)))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-sum$+-definition (equal (apply$-warrant-sum$+) (let ((args (apply$-warrant-sum$+-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'sum$+) '(apply$-badge 3 1 :fn nil nil)) (equal (apply$-userfn 'sum$+ args) (sum$+ (car args) (car (cdr args)) (car (cdr (cdr args))))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-sum$+-ac-definition (equal (apply$-warrant-sum$+-ac) (let ((args (apply$-warrant-sum$+-ac-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'sum$+-ac) '(apply$-badge 4 1 :fn nil nil nil)) (equal (apply$-userfn 'sum$+-ac args) (sum$+-ac (car args) (car (cdr args)) (car (cdr (cdr args))) (car (cdr (cdr (cdr args)))))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-sum$-definition (equal (apply$-warrant-sum$) (let ((args (apply$-warrant-sum$-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'sum$) '(apply$-badge 2 1 :fn nil)) (equal (apply$-userfn 'sum$ args) (sum$ (car args) (car (cdr args)))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-sum$-ac-definition (equal (apply$-warrant-sum$-ac) (let ((args (apply$-warrant-sum$-ac-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'sum$-ac) '(apply$-badge 3 1 :fn nil nil)) (equal (apply$-userfn 'sum$-ac args) (sum$-ac (car args) (car (cdr args)) (car (cdr (cdr args))))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-when$+-definition (equal (apply$-warrant-when$+) (let ((args (apply$-warrant-when$+-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'when$+) '(apply$-badge 3 1 :fn nil nil)) (equal (apply$-userfn 'when$+ args) (when$+ (car args) (car (cdr args)) (car (cdr (cdr args))))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-when$+-ac-definition (equal (apply$-warrant-when$+-ac) (let ((args (apply$-warrant-when$+-ac-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'when$+-ac) '(apply$-badge 4 1 :fn nil nil nil)) (equal (apply$-userfn 'when$+-ac args) (when$+-ac (car args) (car (cdr args)) (car (cdr (cdr args))) (car (cdr (cdr (cdr args)))))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-when$-definition (equal (apply$-warrant-when$) (let ((args (apply$-warrant-when$-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'when$) '(apply$-badge 2 1 :fn nil)) (equal (apply$-userfn 'when$ args) (when$ (car args) (car (cdr args)))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-when$-ac-definition (equal (apply$-warrant-when$-ac) (let ((args (apply$-warrant-when$-ac-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'when$-ac) '(apply$-badge 3 1 :fn nil nil)) (equal (apply$-userfn 'when$-ac args) (when$-ac (car args) (car (cdr args)) (car (cdr (cdr args))))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-until$+-definition (equal (apply$-warrant-until$+) (let ((args (apply$-warrant-until$+-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'until$+) '(apply$-badge 3 1 :fn nil nil)) (equal (apply$-userfn 'until$+ args) (until$+ (car args) (car (cdr args)) (car (cdr (cdr args))))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-until$+-ac-definition (equal (apply$-warrant-until$+-ac) (let ((args (apply$-warrant-until$+-ac-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'until$+-ac) '(apply$-badge 4 1 :fn nil nil nil)) (equal (apply$-userfn 'until$+-ac args) (until$+-ac (car args) (car (cdr args)) (car (cdr (cdr args))) (car (cdr (cdr (cdr args)))))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-until$-definition (equal (apply$-warrant-until$) (let ((args (apply$-warrant-until$-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'until$) '(apply$-badge 2 1 :fn nil)) (equal (apply$-userfn 'until$ args) (until$ (car args) (car (cdr args)))))))) :rule-classes :definition)
Theorem:
(defthm apply$-warrant-until$-ac-definition (equal (apply$-warrant-until$-ac) (let ((args (apply$-warrant-until$-ac-witness))) (implies (tamep-functionp (car args)) (and (equal (badge-userfn 'until$-ac) '(apply$-badge 3 1 :fn nil nil)) (equal (apply$-userfn 'until$-ac args) (until$-ac (car args) (car (cdr args)) (car (cdr (cdr args))))))))) :rule-classes :definition)