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Rewriting-concatenations

Svex-normalize-concats

Signature
(svex-normalize-concats x) → new-x
Arguments: x — Guard (svex-p x).
Returns: new-x — Type (svex-p new-x).

Definitions and Theorems

Function: svex-normalize-concats

(defun svex-normalize-concats (x)
  (declare (xargs :guard (svex-p x)))
  (let ((__function__ 'svex-normalize-concats))
    (declare (ignorable __function__))
    (b* ((ctxalist (svexlist-make-top-context-alist (list x)
                                                    nil))
         (res (svex-normalize-concats-aux x ctxalist)))
      (clear-memoize-table 'svex-normalize-concats-aux)
      (fast-alist-free ctxalist)
      res)))

Theorem: svex-p-of-svex-normalize-concats

(defthm svex-p-of-svex-normalize-concats
  (b* ((new-x (svex-normalize-concats x)))
    (svex-p new-x))
  :rule-classes :rewrite)

Theorem: svex-normalize-concats-correct

(defthm svex-normalize-concats-correct
  (b* ((?new-x (svex-normalize-concats x)))
    (equal (svex-eval new-x env)
           (svex-eval x env))))

Theorem: vars-of-svex-normalize-concats

(defthm vars-of-svex-normalize-concats
  (b* ((?new-x (svex-normalize-concats x)))
    (implies (not (member v (svex-vars x)))
             (not (member v (svex-vars new-x))))))

Theorem: svex-normalize-concats-of-svex-fix-x

(defthm svex-normalize-concats-of-svex-fix-x
  (equal (svex-normalize-concats (svex-fix x))
         (svex-normalize-concats x)))

Theorem: svex-normalize-concats-svex-equiv-congruence-on-x

(defthm svex-normalize-concats-svex-equiv-congruence-on-x
  (implies (svex-equiv x x-equiv)
           (equal (svex-normalize-concats x)
                  (svex-normalize-concats x-equiv)))
  :rule-classes :congruence)