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A4veclist-eval

Evaluate a list of a4vecs.

Signature
(a4veclist-eval x env) → vals
Arguments: x — Guard (a4veclist-p x).
Returns: vals — Type (4veclist-p vals).

Definitions and Theorems

Function: a4veclist-eval

(defun a4veclist-eval (x env)
  (declare (xargs :guard (a4veclist-p x)))
  (let ((__function__ 'a4veclist-eval))
    (declare (ignorable __function__))
    (if (atom x)
        nil
      (cons (a4vec-eval (car x) env)
            (a4veclist-eval (cdr x) env)))))

Theorem: 4veclist-p-of-a4veclist-eval

(defthm 4veclist-p-of-a4veclist-eval
  (b* ((vals (a4veclist-eval x env)))
    (4veclist-p vals))
  :rule-classes :rewrite)

Theorem: len-of-a4veclist-eval

(defthm len-of-a4veclist-eval
  (equal (len (a4veclist-eval x env))
         (len x)))

Theorem: a4veclist-eval-of-a4veclist-fix-x

(defthm a4veclist-eval-of-a4veclist-fix-x
  (equal (a4veclist-eval (a4veclist-fix x) env)
         (a4veclist-eval x env)))

Theorem: a4veclist-eval-a4veclist-equiv-congruence-on-x

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