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Cgraph-formula

Cgraph-formula-fix

Fixing function for cgraph-formula structures.

Signature
(cgraph-formula-fix x) → new-x
Arguments: x — Guard (cgraph-formula-p x).
Returns: new-x — Type (cgraph-formula-p new-x).

Definitions and Theorems

Function: cgraph-formula-fix$inline

(defun cgraph-formula-fix$inline (x)
 (declare (xargs :guard (cgraph-formula-p x)))
 (let ((__function__ 'cgraph-formula-fix))
  (declare (ignorable __function__))
  (mbe :logic
       (b* ((deps (fgl-object-bindings-fix (cdr (std::da-nth 0 x))))
            (name (acl2::symbol-fix (cdr (std::da-nth 1 x))))
            (dep-success-vars
                 (pseudo-term-subst-fix (cdr (std::da-nth 2 x))))
            (success (pseudo-term-fix (cdr (std::da-nth 3 x))))
            (priority (pseudo-term-fix (cdr (std::da-nth 4 x))))
            (value (pseudo-term-fix (cdr (std::da-nth 5 x))))
            (order (nfix (cdr (std::da-nth 6 x))))
            (ruletype (ctrex-ruletype-fix (cdr (std::da-nth 7 x)))))
         (list (cons 'deps deps)
               (cons 'name name)
               (cons 'dep-success-vars
                     dep-success-vars)
               (cons 'success success)
               (cons 'priority priority)
               (cons 'value value)
               (cons 'order order)
               (cons 'ruletype ruletype)))
       :exec x)))

Theorem: cgraph-formula-p-of-cgraph-formula-fix

(defthm cgraph-formula-p-of-cgraph-formula-fix
  (b* ((new-x (cgraph-formula-fix$inline x)))
    (cgraph-formula-p new-x))
  :rule-classes :rewrite)

Theorem: cgraph-formula-fix-when-cgraph-formula-p

(defthm cgraph-formula-fix-when-cgraph-formula-p
  (implies (cgraph-formula-p x)
           (equal (cgraph-formula-fix x) x)))

Function: cgraph-formula-equiv$inline

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

Theorem: cgraph-formula-equiv-is-an-equivalence

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

Theorem: cgraph-formula-equiv-implies-equal-cgraph-formula-fix-1

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

Theorem: cgraph-formula-fix-under-cgraph-formula-equiv

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

Theorem: equal-of-cgraph-formula-fix-1-forward-to-cgraph-formula-equiv

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

Theorem: equal-of-cgraph-formula-fix-2-forward-to-cgraph-formula-equiv

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

Theorem: cgraph-formula-equiv-of-cgraph-formula-fix-1-forward

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

Theorem: cgraph-formula-equiv-of-cgraph-formula-fix-2-forward

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