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• Aignet-output-range-map

Aignet-output-range-map-fix

(aignet-output-range-map-fix x) is an ACL2::fty alist fixing function that follows the fix-keys strategy.

Signature

(aignet-output-range-map-fix x) → fty::newx

Arguments

x — Guard (aignet-output-range-map-p x).

Returns

fty::newx — Type (aignet-output-range-map-p fty::newx).

Note that in the execution this is just an inline identity function.

Definitions and Theorems

Function: aignet-output-range-map-fix$inline

(defun aignet-output-range-map-fix$inline (x)
  (declare (xargs :guard (aignet-output-range-map-p x)))
  (let ((__function__ 'aignet-output-range-map-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom x)
             nil
           (if (consp (car x))
               (cons (cons (acl2::symbol-fix (caar x))
                           (nfix (cdar x)))
                     (aignet-output-range-map-fix (cdr x)))
             (aignet-output-range-map-fix (cdr x))))
         :exec x)))

Theorem: aignet-output-range-map-p-of-aignet-output-range-map-fix

(defthm aignet-output-range-map-p-of-aignet-output-range-map-fix
  (b* ((fty::newx (aignet-output-range-map-fix$inline x)))
    (aignet-output-range-map-p fty::newx))
  :rule-classes :rewrite)

Theorem: aignet-output-range-map-fix-when-aignet-output-range-map-p

(defthm aignet-output-range-map-fix-when-aignet-output-range-map-p
  (implies (aignet-output-range-map-p x)
           (equal (aignet-output-range-map-fix x)
                  x)))

Function: aignet-output-range-map-equiv$inline

(defun aignet-output-range-map-equiv$inline (x acl2::y)
  (declare (xargs :guard (and (aignet-output-range-map-p x)
                              (aignet-output-range-map-p acl2::y))))
  (equal (aignet-output-range-map-fix x)
         (aignet-output-range-map-fix acl2::y)))

Theorem: aignet-output-range-map-equiv-is-an-equivalence

(defthm aignet-output-range-map-equiv-is-an-equivalence
  (and (booleanp (aignet-output-range-map-equiv x y))
       (aignet-output-range-map-equiv x x)
       (implies (aignet-output-range-map-equiv x y)
                (aignet-output-range-map-equiv y x))
       (implies (and (aignet-output-range-map-equiv x y)
                     (aignet-output-range-map-equiv y z))
                (aignet-output-range-map-equiv x z)))
  :rule-classes (:equivalence))

Theorem: aignet-output-range-map-equiv-implies-equal-aignet-output-range-map-fix-1

(defthm
 aignet-output-range-map-equiv-implies-equal-aignet-output-range-map-fix-1
 (implies (aignet-output-range-map-equiv x x-equiv)
          (equal (aignet-output-range-map-fix x)
                 (aignet-output-range-map-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: aignet-output-range-map-fix-under-aignet-output-range-map-equiv

(defthm
    aignet-output-range-map-fix-under-aignet-output-range-map-equiv
  (aignet-output-range-map-equiv (aignet-output-range-map-fix x)
                                 x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-aignet-output-range-map-fix-1-forward-to-aignet-output-range-map-equiv

(defthm
 equal-of-aignet-output-range-map-fix-1-forward-to-aignet-output-range-map-equiv
 (implies (equal (aignet-output-range-map-fix x)
                 acl2::y)
          (aignet-output-range-map-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-aignet-output-range-map-fix-2-forward-to-aignet-output-range-map-equiv

(defthm
 equal-of-aignet-output-range-map-fix-2-forward-to-aignet-output-range-map-equiv
 (implies (equal x (aignet-output-range-map-fix acl2::y))
          (aignet-output-range-map-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: aignet-output-range-map-equiv-of-aignet-output-range-map-fix-1-forward

(defthm
 aignet-output-range-map-equiv-of-aignet-output-range-map-fix-1-forward
 (implies
      (aignet-output-range-map-equiv (aignet-output-range-map-fix x)
                                     acl2::y)
      (aignet-output-range-map-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: aignet-output-range-map-equiv-of-aignet-output-range-map-fix-2-forward

(defthm
 aignet-output-range-map-equiv-of-aignet-output-range-map-fix-2-forward
 (implies (aignet-output-range-map-equiv
               x (aignet-output-range-map-fix acl2::y))
          (aignet-output-range-map-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: cons-of-symbol-fix-k-under-aignet-output-range-map-equiv

(defthm cons-of-symbol-fix-k-under-aignet-output-range-map-equiv
  (aignet-output-range-map-equiv
       (cons (cons (acl2::symbol-fix acl2::k)
                   acl2::v)
             x)
       (cons (cons acl2::k acl2::v) x)))

Theorem: cons-symbol-equiv-congruence-on-k-under-aignet-output-range-map-equiv

(defthm
 cons-symbol-equiv-congruence-on-k-under-aignet-output-range-map-equiv
 (implies
    (acl2::symbol-equiv acl2::k k-equiv)
    (aignet-output-range-map-equiv (cons (cons acl2::k acl2::v) x)
                                   (cons (cons k-equiv acl2::v) x)))
 :rule-classes :congruence)

Theorem: cons-of-nfix-v-under-aignet-output-range-map-equiv

(defthm cons-of-nfix-v-under-aignet-output-range-map-equiv
  (aignet-output-range-map-equiv
       (cons (cons acl2::k (nfix acl2::v)) x)
       (cons (cons acl2::k acl2::v) x)))

Theorem: cons-nat-equiv-congruence-on-v-under-aignet-output-range-map-equiv

(defthm
 cons-nat-equiv-congruence-on-v-under-aignet-output-range-map-equiv
 (implies
    (nat-equiv acl2::v v-equiv)
    (aignet-output-range-map-equiv (cons (cons acl2::k acl2::v) x)
                                   (cons (cons acl2::k v-equiv) x)))
 :rule-classes :congruence)

Theorem: cons-of-aignet-output-range-map-fix-y-under-aignet-output-range-map-equiv

(defthm
 cons-of-aignet-output-range-map-fix-y-under-aignet-output-range-map-equiv
 (aignet-output-range-map-equiv
      (cons x (aignet-output-range-map-fix acl2::y))
      (cons x acl2::y)))

Theorem: cons-aignet-output-range-map-equiv-congruence-on-y-under-aignet-output-range-map-equiv

(defthm
 cons-aignet-output-range-map-equiv-congruence-on-y-under-aignet-output-range-map-equiv
 (implies (aignet-output-range-map-equiv acl2::y y-equiv)
          (aignet-output-range-map-equiv (cons x acl2::y)
                                         (cons x y-equiv)))
 :rule-classes :congruence)

Theorem: aignet-output-range-map-fix-of-acons

(defthm aignet-output-range-map-fix-of-acons
  (equal
       (aignet-output-range-map-fix (cons (cons acl2::a acl2::b) x))
       (cons (cons (acl2::symbol-fix acl2::a)
                   (nfix acl2::b))
             (aignet-output-range-map-fix x))))

Theorem: aignet-output-range-map-fix-of-append

(defthm aignet-output-range-map-fix-of-append
  (equal (aignet-output-range-map-fix (append std::a std::b))
         (append (aignet-output-range-map-fix std::a)
                 (aignet-output-range-map-fix std::b))))

Theorem: consp-car-of-aignet-output-range-map-fix

(defthm consp-car-of-aignet-output-range-map-fix
  (equal (consp (car (aignet-output-range-map-fix x)))
         (consp (aignet-output-range-map-fix x))))