		Search-engine friendly clone of the ACL2 documentation.

Svex-argmasks

Svmask-for-resand

Implements svex-argmasks for RESAND.

Signature
(svmask-for-resand mask args) → argmasks
Arguments: mask — Care mask for the full expression.
Guard (4vmask-p mask).; args — Arguments to this RESAND operator.
Guard (svexlist-p args).
Returns: argmasks — The new care masks inferred for the args.
Type (4vmasklist-p argmasks).

See svmask-for-bitand; the same analysis applies equally well to (resand x y).

Definitions and Theorems

Function: svmask-for-resand$inline

(defun svmask-for-resand$inline (mask args)
  (declare (xargs :guard (and (4vmask-p mask)
                              (svexlist-p args))))
  (let ((__function__ 'svmask-for-resand))
    (declare (ignorable __function__))
    (b* ((mask (4vmask-fix mask)))
      (svmask-for-bitand mask args))))

Theorem: 4vmasklist-p-of-svmask-for-resand

(defthm 4vmasklist-p-of-svmask-for-resand
  (b* ((argmasks (svmask-for-resand$inline mask args)))
    (4vmasklist-p argmasks))
  :rule-classes :rewrite)

Theorem: svmask-for-resand$inline-of-4vmask-fix-mask

(defthm svmask-for-resand$inline-of-4vmask-fix-mask
  (equal (svmask-for-resand$inline (4vmask-fix mask)
                                   args)
         (svmask-for-resand$inline mask args)))

Theorem: svmask-for-resand$inline-4vmask-equiv-congruence-on-mask

(defthm svmask-for-resand$inline-4vmask-equiv-congruence-on-mask
  (implies (4vmask-equiv mask mask-equiv)
           (equal (svmask-for-resand$inline mask args)
                  (svmask-for-resand$inline mask-equiv args)))
  :rule-classes :congruence)

Theorem: svmask-for-resand$inline-of-svexlist-fix-args

(defthm svmask-for-resand$inline-of-svexlist-fix-args
  (equal (svmask-for-resand$inline mask (svexlist-fix args))
         (svmask-for-resand$inline mask args)))

Theorem: svmask-for-resand$inline-svexlist-equiv-congruence-on-args

(defthm svmask-for-resand$inline-svexlist-equiv-congruence-on-args
  (implies (svexlist-equiv args args-equiv)
           (equal (svmask-for-resand$inline mask args)
                  (svmask-for-resand$inline mask args-equiv)))
  :rule-classes :congruence)

Theorem: svmask-for-resand-correct

(defthm svmask-for-resand-correct
 (implies
    (and (equal (4veclist-mask (svmask-for-resand mask args)
                               (svexlist-eval args env))
                (4veclist-mask (svmask-for-resand mask args)
                               args1))
         (syntaxp (not (equal args1
                              (cons 'svexlist-eval
                                    (cons args (cons env 'nil)))))))
    (equal (4vec-mask mask (svex-apply 'resand args1))
           (4vec-mask mask
                      (svex-apply 'resand
                                  (svexlist-eval args env))))))