		Search-engine friendly clone of the ACL2 documentation.

Constdecl

Constdecl-fix

Fixing function for constdecl structures.

Signature
(constdecl-fix x) → new-x
Arguments: x — Guard (constdeclp x).
Returns: new-x — Type (constdeclp new-x).

Definitions and Theorems

Function: constdecl-fix$inline

(defun constdecl-fix$inline (x)
  (declare (xargs :guard (constdeclp x)))
  (let ((__function__ 'constdecl-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((name (identifier-fix (cdr (std::da-nth 0 (cdr x)))))
              (type (type-fix (cdr (std::da-nth 1 (cdr x)))))
              (init (expression-fix (cdr (std::da-nth 2 (cdr x))))))
           (cons :constdecl (list (cons 'name name)
                                  (cons 'type type)
                                  (cons 'init init))))
         :exec x)))

Theorem: constdeclp-of-constdecl-fix

(defthm constdeclp-of-constdecl-fix
  (b* ((new-x (constdecl-fix$inline x)))
    (constdeclp new-x))
  :rule-classes :rewrite)

Theorem: constdecl-fix-when-constdeclp

(defthm constdecl-fix-when-constdeclp
  (implies (constdeclp x)
           (equal (constdecl-fix x) x)))

Function: constdecl-equiv$inline

(defun constdecl-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (constdeclp acl2::x)
                              (constdeclp acl2::y))))
  (equal (constdecl-fix acl2::x)
         (constdecl-fix acl2::y)))

Theorem: constdecl-equiv-is-an-equivalence

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

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

(defthm constdecl-equiv-implies-equal-constdecl-fix-1
  (implies (constdecl-equiv acl2::x x-equiv)
           (equal (constdecl-fix acl2::x)
                  (constdecl-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: constdecl-fix-under-constdecl-equiv

(defthm constdecl-fix-under-constdecl-equiv
  (constdecl-equiv (constdecl-fix acl2::x)
                   acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

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

(defthm equal-of-constdecl-fix-1-forward-to-constdecl-equiv
  (implies (equal (constdecl-fix acl2::x) acl2::y)
           (constdecl-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm equal-of-constdecl-fix-2-forward-to-constdecl-equiv
  (implies (equal acl2::x (constdecl-fix acl2::y))
           (constdecl-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm constdecl-equiv-of-constdecl-fix-1-forward
  (implies (constdecl-equiv (constdecl-fix acl2::x)
                            acl2::y)
           (constdecl-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm constdecl-equiv-of-constdecl-fix-2-forward
  (implies (constdecl-equiv acl2::x (constdecl-fix acl2::y))
           (constdecl-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)