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• Svstmt-writelist

Svstmt-writelist-fix

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

Signature

(svstmt-writelist-fix x) → fty::newx

Arguments

x — Guard (svstmt-writelist-p x).

Returns

fty::newx — Type (svstmt-writelist-p fty::newx).

In the logic, we apply svstmt-write-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: svstmt-writelist-fix$inline

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

Theorem: svstmt-writelist-p-of-svstmt-writelist-fix

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

Theorem: svstmt-writelist-fix-when-svstmt-writelist-p

(defthm svstmt-writelist-fix-when-svstmt-writelist-p
  (implies (svstmt-writelist-p x)
           (equal (svstmt-writelist-fix x) x)))

Function: svstmt-writelist-equiv$inline

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

Theorem: svstmt-writelist-equiv-is-an-equivalence

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

Theorem: svstmt-writelist-equiv-implies-equal-svstmt-writelist-fix-1

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

Theorem: svstmt-writelist-fix-under-svstmt-writelist-equiv

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

Theorem: equal-of-svstmt-writelist-fix-1-forward-to-svstmt-writelist-equiv

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

Theorem: equal-of-svstmt-writelist-fix-2-forward-to-svstmt-writelist-equiv

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

Theorem: svstmt-writelist-equiv-of-svstmt-writelist-fix-1-forward

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

Theorem: svstmt-writelist-equiv-of-svstmt-writelist-fix-2-forward

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

Theorem: car-of-svstmt-writelist-fix-x-under-svstmt-write-equiv

(defthm car-of-svstmt-writelist-fix-x-under-svstmt-write-equiv
  (svstmt-write-equiv (car (svstmt-writelist-fix x))
                      (car x)))

Theorem: car-svstmt-writelist-equiv-congruence-on-x-under-svstmt-write-equiv

(defthm
 car-svstmt-writelist-equiv-congruence-on-x-under-svstmt-write-equiv
 (implies (svstmt-writelist-equiv x x-equiv)
          (svstmt-write-equiv (car x)
                              (car x-equiv)))
 :rule-classes :congruence)

Theorem: cdr-of-svstmt-writelist-fix-x-under-svstmt-writelist-equiv

(defthm cdr-of-svstmt-writelist-fix-x-under-svstmt-writelist-equiv
  (svstmt-writelist-equiv (cdr (svstmt-writelist-fix x))
                          (cdr x)))

Theorem: cdr-svstmt-writelist-equiv-congruence-on-x-under-svstmt-writelist-equiv

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

Theorem: cons-of-svstmt-write-fix-x-under-svstmt-writelist-equiv

(defthm cons-of-svstmt-write-fix-x-under-svstmt-writelist-equiv
  (svstmt-writelist-equiv (cons (svstmt-write-fix x) y)
                          (cons x y)))

Theorem: cons-svstmt-write-equiv-congruence-on-x-under-svstmt-writelist-equiv

(defthm
 cons-svstmt-write-equiv-congruence-on-x-under-svstmt-writelist-equiv
 (implies (svstmt-write-equiv x x-equiv)
          (svstmt-writelist-equiv (cons x y)
                                  (cons x-equiv y)))
 :rule-classes :congruence)

Theorem: cons-of-svstmt-writelist-fix-y-under-svstmt-writelist-equiv

(defthm cons-of-svstmt-writelist-fix-y-under-svstmt-writelist-equiv
  (svstmt-writelist-equiv (cons x (svstmt-writelist-fix y))
                          (cons x y)))

Theorem: cons-svstmt-writelist-equiv-congruence-on-y-under-svstmt-writelist-equiv

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

Theorem: consp-of-svstmt-writelist-fix

(defthm consp-of-svstmt-writelist-fix
  (equal (consp (svstmt-writelist-fix x))
         (consp x)))

Theorem: svstmt-writelist-fix-of-cons

(defthm svstmt-writelist-fix-of-cons
  (equal (svstmt-writelist-fix (cons a x))
         (cons (svstmt-write-fix a)
               (svstmt-writelist-fix x))))

Theorem: len-of-svstmt-writelist-fix

(defthm len-of-svstmt-writelist-fix
  (equal (len (svstmt-writelist-fix x))
         (len x)))

Theorem: svstmt-writelist-fix-of-append

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

Theorem: svstmt-writelist-fix-of-repeat

(defthm svstmt-writelist-fix-of-repeat
  (equal (svstmt-writelist-fix (repeat acl2::n x))
         (repeat acl2::n (svstmt-write-fix x))))

Theorem: nth-of-svstmt-writelist-fix

(defthm nth-of-svstmt-writelist-fix
  (equal (nth acl2::n (svstmt-writelist-fix x))
         (if (< (nfix acl2::n) (len x))
             (svstmt-write-fix (nth acl2::n x))
           nil)))

Theorem: svstmt-writelist-equiv-implies-svstmt-writelist-equiv-append-1

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

Theorem: svstmt-writelist-equiv-implies-svstmt-writelist-equiv-append-2

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

Theorem: svstmt-writelist-equiv-implies-svstmt-writelist-equiv-nthcdr-2

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

Theorem: svstmt-writelist-equiv-implies-svstmt-writelist-equiv-take-2

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