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Svexlist-maybe-rewrite-fixpoint

Signature

(svexlist-maybe-rewrite-fixpoint x do-rewrite &key (count '4) 
                                 (verbosep 'nil)) 
 
  → 
xx

Arguments

x — Guard (svexlist-p x).

count — Guard (natp count).

Returns

xx — Type (svexlist-p xx).

Definitions and Theorems

Function: svexlist-maybe-rewrite-fixpoint-fn

(defun svexlist-maybe-rewrite-fixpoint-fn
       (x do-rewrite count verbosep)
  (declare (xargs :guard (and (svexlist-p x) (natp count))))
  (let ((__function__ 'svexlist-maybe-rewrite-fixpoint))
    (declare (ignorable __function__))
    (if do-rewrite (svexlist-rewrite-fixpoint x
                                              :count count
                                              :verbosep verbosep)
      (svexlist-fix x))))

Theorem: svexlist-p-of-svexlist-maybe-rewrite-fixpoint

(defthm svexlist-p-of-svexlist-maybe-rewrite-fixpoint
  (b* ((xx (svexlist-maybe-rewrite-fixpoint-fn
                x do-rewrite count verbosep)))
    (svexlist-p xx))
  :rule-classes :rewrite)

Theorem: svexlist-maybe-rewrite-fixpoint-fn-of-svexlist-fix-x

(defthm svexlist-maybe-rewrite-fixpoint-fn-of-svexlist-fix-x
 (equal
  (svexlist-maybe-rewrite-fixpoint-fn (svexlist-fix x)
                                      do-rewrite count verbosep)
  (svexlist-maybe-rewrite-fixpoint-fn x do-rewrite count verbosep)))

Theorem: svexlist-maybe-rewrite-fixpoint-fn-svexlist-equiv-congruence-on-x

(defthm
  svexlist-maybe-rewrite-fixpoint-fn-svexlist-equiv-congruence-on-x
 (implies
  (svexlist-equiv x x-equiv)
  (equal
    (svexlist-maybe-rewrite-fixpoint-fn x do-rewrite count verbosep)
    (svexlist-maybe-rewrite-fixpoint-fn
         x-equiv do-rewrite count verbosep)))
 :rule-classes :congruence)

Theorem: svexlist-maybe-rewrite-fixpoint-fn-of-nfix-count

(defthm svexlist-maybe-rewrite-fixpoint-fn-of-nfix-count
 (equal
  (svexlist-maybe-rewrite-fixpoint-fn x do-rewrite (nfix count)
                                      verbosep)
  (svexlist-maybe-rewrite-fixpoint-fn x do-rewrite count verbosep)))

Theorem: svexlist-maybe-rewrite-fixpoint-fn-nat-equiv-congruence-on-count

(defthm
   svexlist-maybe-rewrite-fixpoint-fn-nat-equiv-congruence-on-count
 (implies
  (nat-equiv count count-equiv)
  (equal
    (svexlist-maybe-rewrite-fixpoint-fn x do-rewrite count verbosep)
    (svexlist-maybe-rewrite-fixpoint-fn
         x do-rewrite count-equiv verbosep)))
 :rule-classes :congruence)

Theorem: svexlist-maybe-rewrite-fixpoint-correct

(defthm svexlist-maybe-rewrite-fixpoint-correct
  (b* ((?xx (svexlist-maybe-rewrite-fixpoint-fn
                 x do-rewrite count verbosep)))
    (equal (svexlist-eval xx env)
           (svexlist-eval x env))))

Theorem: len-of-svexlist-maybe-rewrite-fixpoint

(defthm len-of-svexlist-maybe-rewrite-fixpoint
  (b* ((?xx (svexlist-maybe-rewrite-fixpoint-fn
                 x do-rewrite count verbosep)))
    (equal (len xx) (len x))))

Theorem: consp-of-svexlist-maybe-rewrite-fixpoint

(defthm consp-of-svexlist-maybe-rewrite-fixpoint
  (b* ((?xx (svexlist-maybe-rewrite-fixpoint-fn
                 x do-rewrite count verbosep)))
    (equal (consp xx) (consp x))))

Theorem: vars-of-svexlist-maybe-rewrite-fixpoint

(defthm vars-of-svexlist-maybe-rewrite-fixpoint
  (b* ((?xx (svexlist-maybe-rewrite-fixpoint-fn
                 x do-rewrite count verbosep)))
    (implies (not (member v (svexlist-vars x)))
             (not (member v (svexlist-vars xx))))))