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Fgl-generic-rule

Fgl-generic-rule-fix

(fgl-generic-rule-fix x) is a ACL2::fty fixing function.

Signature
(fgl-generic-rule-fix x) → fty::newx
Arguments: x — Guard (fgl-generic-rule-p x).
Returns: fty::newx — Type (fgl-generic-rule-p fty::newx).

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

Definitions and Theorems

Function: fgl-generic-rule-fix$inline

(defun fgl-generic-rule-fix$inline (x)
  (declare (xargs :guard (fgl-generic-rule-p x)))
  (let ((__function__ 'fgl-generic-rule-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (tag x)
           ((:brewrite :bmeta)
            (fgl-binder-rule-fix x))
           (otherwise (fgl-rule-fix x)))
         :exec x)))

Theorem: fgl-generic-rule-p-of-fgl-generic-rule-fix

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

Theorem: fgl-generic-rule-fix-when-fgl-generic-rule-p

(defthm fgl-generic-rule-fix-when-fgl-generic-rule-p
  (implies (fgl-generic-rule-p x)
           (equal (fgl-generic-rule-fix x) x)))

Function: fgl-generic-rule-equiv$inline

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

Theorem: fgl-generic-rule-equiv-is-an-equivalence

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

Theorem: fgl-generic-rule-equiv-implies-equal-fgl-generic-rule-fix-1

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

Theorem: fgl-generic-rule-fix-under-fgl-generic-rule-equiv

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

Theorem: equal-of-fgl-generic-rule-fix-1-forward-to-fgl-generic-rule-equiv

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

Theorem: equal-of-fgl-generic-rule-fix-2-forward-to-fgl-generic-rule-equiv

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

Theorem: fgl-generic-rule-equiv-of-fgl-generic-rule-fix-1-forward

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

Theorem: fgl-generic-rule-equiv-of-fgl-generic-rule-fix-2-forward

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

Theorem: tag-of-fgl-generic-rule-fix-forward

(defthm tag-of-fgl-generic-rule-fix-forward
  (or (equal (tag (fgl-generic-rule-fix x))
             :brewrite)
      (equal (tag (fgl-generic-rule-fix x))
             :bmeta)
      (equal (tag (fgl-generic-rule-fix x))
             :rewrite)
      (equal (tag (fgl-generic-rule-fix x))
             :primitive)
      (equal (tag (fgl-generic-rule-fix x))
             :meta))
  :rule-classes
  ((:forward-chaining
        :trigger-terms ((tag (fgl-generic-rule-fix x))))))