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• Modnamelist

Modnamelist-fix

(modnamelist-fix x) is a usual fty list fixing function.

Signature

(modnamelist-fix x) → fty::newx

Arguments

x — Guard (modnamelist-p x).

Returns

fty::newx — Type (modnamelist-p fty::newx).

In the logic, we apply modname-fix to each member of the x. In the execution, none of that is actually necessary and this is just an inlined identity function.

Definitions and Theorems

Function: modnamelist-fix$inline

(defun modnamelist-fix$inline (x)
  (declare (xargs :guard (modnamelist-p x)))
  (let ((__function__ 'modnamelist-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom x)
             nil
           (cons (modname-fix (car x))
                 (modnamelist-fix (cdr x))))
         :exec x)))

Theorem: modnamelist-p-of-modnamelist-fix

(defthm modnamelist-p-of-modnamelist-fix
  (b* ((fty::newx (modnamelist-fix$inline x)))
    (modnamelist-p fty::newx))
  :rule-classes :rewrite)

Theorem: modnamelist-fix-when-modnamelist-p

(defthm modnamelist-fix-when-modnamelist-p
  (implies (modnamelist-p x)
           (equal (modnamelist-fix x) x)))

Function: modnamelist-equiv$inline

(defun modnamelist-equiv$inline (x y)
  (declare (xargs :guard (and (modnamelist-p x)
                              (modnamelist-p y))))
  (equal (modnamelist-fix x)
         (modnamelist-fix y)))

Theorem: modnamelist-equiv-is-an-equivalence

(defthm modnamelist-equiv-is-an-equivalence
  (and (booleanp (modnamelist-equiv x y))
       (modnamelist-equiv x x)
       (implies (modnamelist-equiv x y)
                (modnamelist-equiv y x))
       (implies (and (modnamelist-equiv x y)
                     (modnamelist-equiv y z))
                (modnamelist-equiv x z)))
  :rule-classes (:equivalence))

Theorem: modnamelist-equiv-implies-equal-modnamelist-fix-1

(defthm modnamelist-equiv-implies-equal-modnamelist-fix-1
  (implies (modnamelist-equiv x x-equiv)
           (equal (modnamelist-fix x)
                  (modnamelist-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: modnamelist-fix-under-modnamelist-equiv

(defthm modnamelist-fix-under-modnamelist-equiv
  (modnamelist-equiv (modnamelist-fix x)
                     x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-modnamelist-fix-1-forward-to-modnamelist-equiv

(defthm equal-of-modnamelist-fix-1-forward-to-modnamelist-equiv
  (implies (equal (modnamelist-fix x) y)
           (modnamelist-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-modnamelist-fix-2-forward-to-modnamelist-equiv

(defthm equal-of-modnamelist-fix-2-forward-to-modnamelist-equiv
  (implies (equal x (modnamelist-fix y))
           (modnamelist-equiv x y))
  :rule-classes :forward-chaining)

Theorem: modnamelist-equiv-of-modnamelist-fix-1-forward

(defthm modnamelist-equiv-of-modnamelist-fix-1-forward
  (implies (modnamelist-equiv (modnamelist-fix x)
                              y)
           (modnamelist-equiv x y))
  :rule-classes :forward-chaining)

Theorem: modnamelist-equiv-of-modnamelist-fix-2-forward

(defthm modnamelist-equiv-of-modnamelist-fix-2-forward
  (implies (modnamelist-equiv x (modnamelist-fix y))
           (modnamelist-equiv x y))
  :rule-classes :forward-chaining)

Theorem: car-of-modnamelist-fix-x-under-modname-equiv

(defthm car-of-modnamelist-fix-x-under-modname-equiv
  (modname-equiv (car (modnamelist-fix x))
                 (car x)))

Theorem: car-modnamelist-equiv-congruence-on-x-under-modname-equiv

(defthm car-modnamelist-equiv-congruence-on-x-under-modname-equiv
  (implies (modnamelist-equiv x x-equiv)
           (modname-equiv (car x) (car x-equiv)))
  :rule-classes :congruence)

Theorem: cdr-of-modnamelist-fix-x-under-modnamelist-equiv

(defthm cdr-of-modnamelist-fix-x-under-modnamelist-equiv
  (modnamelist-equiv (cdr (modnamelist-fix x))
                     (cdr x)))

Theorem: cdr-modnamelist-equiv-congruence-on-x-under-modnamelist-equiv

(defthm
      cdr-modnamelist-equiv-congruence-on-x-under-modnamelist-equiv
  (implies (modnamelist-equiv x x-equiv)
           (modnamelist-equiv (cdr x)
                              (cdr x-equiv)))
  :rule-classes :congruence)

Theorem: cons-of-modname-fix-x-under-modnamelist-equiv

(defthm cons-of-modname-fix-x-under-modnamelist-equiv
  (modnamelist-equiv (cons (modname-fix x) y)
                     (cons x y)))

Theorem: cons-modname-equiv-congruence-on-x-under-modnamelist-equiv

(defthm cons-modname-equiv-congruence-on-x-under-modnamelist-equiv
  (implies (modname-equiv x x-equiv)
           (modnamelist-equiv (cons x y)
                              (cons x-equiv y)))
  :rule-classes :congruence)

Theorem: cons-of-modnamelist-fix-y-under-modnamelist-equiv

(defthm cons-of-modnamelist-fix-y-under-modnamelist-equiv
  (modnamelist-equiv (cons x (modnamelist-fix y))
                     (cons x y)))

Theorem: cons-modnamelist-equiv-congruence-on-y-under-modnamelist-equiv

(defthm
     cons-modnamelist-equiv-congruence-on-y-under-modnamelist-equiv
  (implies (modnamelist-equiv y y-equiv)
           (modnamelist-equiv (cons x y)
                              (cons x y-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-modnamelist-fix

(defthm consp-of-modnamelist-fix
  (equal (consp (modnamelist-fix x))
         (consp x)))

Theorem: modnamelist-fix-under-iff

(defthm modnamelist-fix-under-iff
  (iff (modnamelist-fix x) (consp x)))

Theorem: modnamelist-fix-of-cons

(defthm modnamelist-fix-of-cons
  (equal (modnamelist-fix (cons a x))
         (cons (modname-fix a)
               (modnamelist-fix x))))

Theorem: len-of-modnamelist-fix

(defthm len-of-modnamelist-fix
  (equal (len (modnamelist-fix x))
         (len x)))

Theorem: modnamelist-fix-of-append

(defthm modnamelist-fix-of-append
  (equal (modnamelist-fix (append std::a std::b))
         (append (modnamelist-fix std::a)
                 (modnamelist-fix std::b))))

Theorem: modnamelist-fix-of-repeat

(defthm modnamelist-fix-of-repeat
  (equal (modnamelist-fix (repeat acl2::n x))
         (repeat acl2::n (modname-fix x))))

Theorem: list-equiv-refines-modnamelist-equiv

(defthm list-equiv-refines-modnamelist-equiv
  (implies (list-equiv x y)
           (modnamelist-equiv x y))
  :rule-classes :refinement)

Theorem: nth-of-modnamelist-fix

(defthm nth-of-modnamelist-fix
  (equal (nth acl2::n (modnamelist-fix x))
         (if (< (nfix acl2::n) (len x))
             (modname-fix (nth acl2::n x))
           nil)))

Theorem: modnamelist-equiv-implies-modnamelist-equiv-append-1

(defthm modnamelist-equiv-implies-modnamelist-equiv-append-1
  (implies (modnamelist-equiv x fty::x-equiv)
           (modnamelist-equiv (append x y)
                              (append fty::x-equiv y)))
  :rule-classes (:congruence))

Theorem: modnamelist-equiv-implies-modnamelist-equiv-append-2

(defthm modnamelist-equiv-implies-modnamelist-equiv-append-2
  (implies (modnamelist-equiv y fty::y-equiv)
           (modnamelist-equiv (append x y)
                              (append x fty::y-equiv)))
  :rule-classes (:congruence))

Theorem: modnamelist-equiv-implies-modnamelist-equiv-nthcdr-2

(defthm modnamelist-equiv-implies-modnamelist-equiv-nthcdr-2
  (implies (modnamelist-equiv acl2::l l-equiv)
           (modnamelist-equiv (nthcdr acl2::n acl2::l)
                              (nthcdr acl2::n l-equiv)))
  :rule-classes (:congruence))

Theorem: modnamelist-equiv-implies-modnamelist-equiv-take-2

(defthm modnamelist-equiv-implies-modnamelist-equiv-take-2
  (implies (modnamelist-equiv acl2::l l-equiv)
           (modnamelist-equiv (take acl2::n acl2::l)
                              (take acl2::n l-equiv)))
  :rule-classes (:congruence))