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• Smtlink-process-user-hint

Hints-syntax

Definitions and Theorems

Function: hints-syntax-p

(defun hints-syntax-p (term)
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'hints-syntax-p))
    (declare (ignorable acl2::__function__))
    (true-listp term)))

Theorem: booleanp-of-hints-syntax-p

(defthm booleanp-of-hints-syntax-p
  (b* ((syntax-good? (hints-syntax-p term)))
    (booleanp syntax-good?))
  :rule-classes :rewrite)

Function: hints-syntax-fix

(defun hints-syntax-fix (term)
  (declare (xargs :guard (hints-syntax-p term)))
  (let ((acl2::__function__ 'hints-syntax-fix))
    (declare (ignorable acl2::__function__))
    (mbe :logic (if (hints-syntax-p term) term nil)
         :exec term)))

Theorem: hints-syntax-p-of-hints-syntax-fix

(defthm hints-syntax-p-of-hints-syntax-fix
  (b* ((fixed-term (hints-syntax-fix term)))
    (hints-syntax-p fixed-term))
  :rule-classes :rewrite)

Function: hints-syntax-equiv$inline

(defun hints-syntax-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (hints-syntax-p acl2::x)
                              (hints-syntax-p acl2::y))))
  (equal (hints-syntax-fix acl2::x)
         (hints-syntax-fix acl2::y)))

Theorem: hints-syntax-equiv-is-an-equivalence

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

Theorem: hints-syntax-equiv-implies-equal-hints-syntax-fix-1

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

Theorem: hints-syntax-fix-under-hints-syntax-equiv

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

Theorem: equal-of-hints-syntax-fix-1-forward-to-hints-syntax-equiv

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

Theorem: equal-of-hints-syntax-fix-2-forward-to-hints-syntax-equiv

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

Theorem: hints-syntax-equiv-of-hints-syntax-fix-1-forward

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

Theorem: hints-syntax-equiv-of-hints-syntax-fix-2-forward

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

Subtopics

Hints-syntax-fix

Fixing function for a hints-sytnax-p.

Hints-syntax-p

Recognizer for hints-syntax.