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Symbolic-arithmetic

Aabf-logeqv-ss

Signature
(aabf-logeqv-ss a b man) → (mv a=b new-man)
Arguments: a — Guard (true-listp a).; b — Guard (true-listp b).

Definitions and Theorems

Function: aabf-logeqv-ss

(defun aabf-logeqv-ss (a b man)
  (declare (xargs :guard (and (true-listp a) (true-listp b))))
  (declare (xargs :guard (and (aabflist-p a man)
                              (aabflist-p b man))))
  (let ((__function__ 'aabf-logeqv-ss))
    (declare (ignorable __function__))
    (b* (((mv af ar aend)
          (aabf-first/rest/end a))
         ((mv bf br bend)
          (aabf-first/rest/end b))
         ((mv c man) (aabf-iff af bf man))
         ((when (and aend bend))
          (mv (list c) man)))
      (aabf-nest (aabf-scons c (aabf-logeqv-ss ar br))
                 man))))

Theorem: trivial-theorem-about-aabf-logeqv-ss

(defthm trivial-theorem-about-aabf-logeqv-ss
  (b* nil
    (b* ((?ignore (aabf-logeqv-ss a b man)))
      t))
  :rule-classes nil)

Theorem: true-listp-of-aabf-logeqv-ss.a=b

(defthm true-listp-of-aabf-logeqv-ss.a=b
  (b* (((mv ?a=b ?new-man)
        (aabf-logeqv-ss a b man)))
    (true-listp a=b))
  :rule-classes :type-prescription)

Theorem: aabf-extension-p-of-aabf-logeqv-ss

(defthm aabf-extension-p-of-aabf-logeqv-ss
  (b* (((mv ?a=b ?new-man)
        (aabf-logeqv-ss a b man)))
    (aabf-extension-p new-man man)))

Theorem: aabf-p-of-aabf-logeqv-ss

(defthm aabf-p-of-aabf-logeqv-ss
  (b* (((mv a=b new-man)
        (aabf-logeqv-ss a b man)))
    (implies (and (aabflist-p a man)
                  (aabflist-p b man))
             (and (aabflist-p a=b new-man)))))

Theorem: aabf-eval-of-aabf-logeqv-ss

(defthm aabf-eval-of-aabf-logeqv-ss
 (b* (((mv a=b new-man)
       (aabf-logeqv-ss a b man)))
  (implies
    (and (aabflist-p a man)
         (aabflist-p b man))
    (and (equal (bools->int (aabflist-eval a=b env new-man))
                (logeqv (bools->int (aabflist-eval a env man))
                        (bools->int (aabflist-eval b env man))))))))

Theorem: aabf-pred-of-aabf-logeqv-ss

(defthm aabf-pred-of-aabf-logeqv-ss
  (b* (((mv a=b new-man)
        (aabf-logeqv-ss a b man)))
    (implies (and (aabflist-p a man)
                  (aabflist-p b man)
                  (aabflist-pred a man)
                  (aabflist-pred b man))
             (and (aabflist-pred a=b new-man)))))