		Search-engine friendly clone of the ACL2 documentation.

Equiv-contextsp

Equiv-contextsp-basics

Basic theorems about equiv-contextsp, generated by std::deflist.

Definitions and Theorems

Theorem: equiv-contextsp-of-cons

(defthm equiv-contextsp-of-cons
  (equal (equiv-contextsp (cons a x))
         (and (pseudo-fnsym-p a)
              (equiv-contextsp x)))
  :rule-classes ((:rewrite)))

Theorem: equiv-contextsp-of-cdr-when-equiv-contextsp

(defthm equiv-contextsp-of-cdr-when-equiv-contextsp
  (implies (equiv-contextsp (double-rewrite x))
           (equiv-contextsp (cdr x)))
  :rule-classes ((:rewrite)))

Theorem: equiv-contextsp-when-not-consp

(defthm equiv-contextsp-when-not-consp
  (implies (not (consp x))
           (equal (equiv-contextsp x) (not x)))
  :rule-classes ((:rewrite)))

Theorem: pseudo-fnsym-p-of-car-when-equiv-contextsp

(defthm pseudo-fnsym-p-of-car-when-equiv-contextsp
  (implies (equiv-contextsp x)
           (iff (pseudo-fnsym-p (car x))
                (or (consp x) (pseudo-fnsym-p nil))))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-equiv-contextsp-compound-recognizer

(defthm true-listp-when-equiv-contextsp-compound-recognizer
  (implies (equiv-contextsp x)
           (true-listp x))
  :rule-classes :compound-recognizer)

Theorem: equiv-contextsp-of-list-fix

(defthm equiv-contextsp-of-list-fix
  (implies (equiv-contextsp x)
           (equiv-contextsp (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: equiv-contextsp-of-append

(defthm equiv-contextsp-of-append
  (equal (equiv-contextsp (append a b))
         (and (equiv-contextsp (list-fix a))
              (equiv-contextsp b)))
  :rule-classes ((:rewrite)))

Theorem: equiv-contextsp-of-take

(defthm equiv-contextsp-of-take
  (implies (equiv-contextsp (double-rewrite x))
           (iff (equiv-contextsp (take n x))
                (or (pseudo-fnsym-p nil)
                    (<= (nfix n) (len x)))))
  :rule-classes ((:rewrite)))

Theorem: equiv-contextsp-of-nthcdr

(defthm equiv-contextsp-of-nthcdr
  (implies (equiv-contextsp (double-rewrite x))
           (equiv-contextsp (nthcdr n x)))
  :rule-classes ((:rewrite)))