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A4veclist/env-list-eval

Signature
(a4veclist/env-list-eval x envs) → 4vecs
Arguments: x — Guard (a4veclistlist-p x).
Returns: 4vecs — Type (4veclistlist-p 4vecs).

Definitions and Theorems

Function: a4veclist/env-list-eval

(defun a4veclist/env-list-eval (x envs)
  (declare (xargs :guard (a4veclistlist-p x)))
  (declare (xargs :guard (equal (len envs) (len x))))
  (let ((__function__ 'a4veclist/env-list-eval))
    (declare (ignorable __function__))
    (if (atom x)
        nil
      (cons (a4veclist-eval (car x) (car envs))
            (a4veclist/env-list-eval (cdr x)
                                     (cdr envs))))))

Theorem: 4veclistlist-p-of-a4veclist/env-list-eval

(defthm 4veclistlist-p-of-a4veclist/env-list-eval
  (b* ((4vecs (a4veclist/env-list-eval x envs)))
    (4veclistlist-p 4vecs))
  :rule-classes :rewrite)

Theorem: a4veclist/env-list-eval-of-a4veclistlist-fix-x

(defthm a4veclist/env-list-eval-of-a4veclistlist-fix-x
  (equal (a4veclist/env-list-eval (a4veclistlist-fix x)
                                  envs)
         (a4veclist/env-list-eval x envs)))

Theorem: a4veclist/env-list-eval-a4veclistlist-equiv-congruence-on-x

(defthm a4veclist/env-list-eval-a4veclistlist-equiv-congruence-on-x
  (implies (a4veclistlist-equiv x x-equiv)
           (equal (a4veclist/env-list-eval x envs)
                  (a4veclist/env-list-eval x-equiv envs)))
  :rule-classes :congruence)