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Rewriting

Svexlist-mask-acons-rev

Signature
(svexlist-mask-acons-rev x mask al) → *
Arguments: x — Guard (svexlist-p x).; mask — Guard (4vmask-p mask).; al — Guard (svex-mask-alist-p al).

Definitions and Theorems

Function: svexlist-mask-acons-rev

(defun svexlist-mask-acons-rev (x mask al)
  (declare (xargs :guard (and (svexlist-p x)
                              (4vmask-p mask)
                              (svex-mask-alist-p al))))
  (let ((__function__ 'svexlist-mask-acons-rev))
    (declare (ignorable __function__))
    (if (atom x)
        (svex-mask-alist-fix al)
      (svexlist-mask-acons-rev (cdr x)
                               mask
                               (svex-mask-acons (car x) mask al)))))

Theorem: svexlist-mask-acons-rev-of-svexlist-fix-x

(defthm svexlist-mask-acons-rev-of-svexlist-fix-x
  (equal (svexlist-mask-acons-rev (svexlist-fix x)
                                  mask al)
         (svexlist-mask-acons-rev x mask al)))

Theorem: svexlist-mask-acons-rev-svexlist-equiv-congruence-on-x

(defthm svexlist-mask-acons-rev-svexlist-equiv-congruence-on-x
  (implies (svexlist-equiv x x-equiv)
           (equal (svexlist-mask-acons-rev x mask al)
                  (svexlist-mask-acons-rev x-equiv mask al)))
  :rule-classes :congruence)

Theorem: svexlist-mask-acons-rev-of-4vmask-fix-mask

(defthm svexlist-mask-acons-rev-of-4vmask-fix-mask
  (equal (svexlist-mask-acons-rev x (4vmask-fix mask)
                                  al)
         (svexlist-mask-acons-rev x mask al)))

Theorem: svexlist-mask-acons-rev-4vmask-equiv-congruence-on-mask

(defthm svexlist-mask-acons-rev-4vmask-equiv-congruence-on-mask
  (implies (4vmask-equiv mask mask-equiv)
           (equal (svexlist-mask-acons-rev x mask al)
                  (svexlist-mask-acons-rev x mask-equiv al)))
  :rule-classes :congruence)

Theorem: svexlist-mask-acons-rev-of-svex-mask-alist-fix-al

(defthm svexlist-mask-acons-rev-of-svex-mask-alist-fix-al
  (equal (svexlist-mask-acons-rev x mask (svex-mask-alist-fix al))
         (svexlist-mask-acons-rev x mask al)))

Theorem: svexlist-mask-acons-rev-svex-mask-alist-equiv-congruence-on-al

(defthm
     svexlist-mask-acons-rev-svex-mask-alist-equiv-congruence-on-al
  (implies (svex-mask-alist-equiv al al-equiv)
           (equal (svexlist-mask-acons-rev x mask al)
                  (svexlist-mask-acons-rev x mask al-equiv)))
  :rule-classes :congruence)