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4vmask-alist

4vmask-acons

Extend a slow 4vmask-alist with a new binding.

Signature
(4vmask-acons var mask alist) → extended-alist
Arguments: var — Variable to bind.
Guard (svar-p var).; mask — Mask to bind it to.
Guard (4vmask-p mask).; alist — Initial alist to extend.
Guard (4vmask-alist-p alist).
Returns: extended-alist — Type (4vmask-alist-p extended-alist).

Definitions and Theorems

Function: 4vmask-acons

(defun 4vmask-acons (var mask alist)
  (declare (xargs :guard (and (svar-p var)
                              (4vmask-p mask)
                              (4vmask-alist-p alist))))
  (let ((__function__ '4vmask-acons))
    (declare (ignorable __function__))
    (mbe :logic (cons (cons (svar-fix var) (4vmask-fix mask))
                      (4vmask-alist-fix alist))
         :exec (acons var mask alist))))

Theorem: 4vmask-alist-p-of-4vmask-acons

(defthm 4vmask-alist-p-of-4vmask-acons
  (b* ((extended-alist (4vmask-acons var mask alist)))
    (4vmask-alist-p extended-alist))
  :rule-classes :rewrite)

Theorem: 4vmask-acons-of-svar-fix-var

(defthm 4vmask-acons-of-svar-fix-var
  (equal (4vmask-acons (svar-fix var) mask alist)
         (4vmask-acons var mask alist)))

Theorem: 4vmask-acons-svar-equiv-congruence-on-var

(defthm 4vmask-acons-svar-equiv-congruence-on-var
  (implies (svar-equiv var var-equiv)
           (equal (4vmask-acons var mask alist)
                  (4vmask-acons var-equiv mask alist)))
  :rule-classes :congruence)

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

(defthm 4vmask-acons-of-4vmask-fix-mask
  (equal (4vmask-acons var (4vmask-fix mask)
                       alist)
         (4vmask-acons var mask alist)))

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

(defthm 4vmask-acons-4vmask-equiv-congruence-on-mask
  (implies (4vmask-equiv mask mask-equiv)
           (equal (4vmask-acons var mask alist)
                  (4vmask-acons var mask-equiv alist)))
  :rule-classes :congruence)

Theorem: 4vmask-acons-of-4vmask-alist-fix-alist

(defthm 4vmask-acons-of-4vmask-alist-fix-alist
  (equal (4vmask-acons var mask (4vmask-alist-fix alist))
         (4vmask-acons var mask alist)))

Theorem: 4vmask-acons-4vmask-alist-equiv-congruence-on-alist

(defthm 4vmask-acons-4vmask-alist-equiv-congruence-on-alist
  (implies (4vmask-alist-equiv alist alist-equiv)
           (equal (4vmask-acons var mask alist)
                  (4vmask-acons var mask alist-equiv)))
  :rule-classes :congruence)

Theorem: 4vmask-assoc-of-4vmask-acons

(defthm 4vmask-assoc-of-4vmask-acons
  (equal (4vmask-assoc j (4vmask-acons k v x))
         (if (svar-equiv j k)
             (4vmask-fix v)
           (4vmask-assoc j x))))