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• Cgraph-edge

Cgraph-edge-fix

Fixing function for cgraph-edge structures.

Signature

(cgraph-edge-fix x) → new-x

Arguments

x — Guard (cgraph-edge-p x).

Returns

new-x — Type (cgraph-edge-p new-x).

Definitions and Theorems

Function: cgraph-edge-fix$inline

(defun cgraph-edge-fix$inline (x)
 (declare (xargs :guard (cgraph-edge-p x)))
 (let ((__function__ 'cgraph-edge-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((match-vars (pseudo-var-list-fix (std::prod-car x)))
     (rule (ctrex-rule-fix (std::prod-car (std::prod-cdr x))))
     (subst
       (fgl-object-bindings-fix (std::prod-cdr (std::prod-cdr x)))))
    (std::prod-cons match-vars (std::prod-cons rule subst)))
   :exec x)))

Theorem: cgraph-edge-p-of-cgraph-edge-fix

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

Theorem: cgraph-edge-fix-when-cgraph-edge-p

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

Function: cgraph-edge-equiv$inline

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

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

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

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

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

Theorem: cgraph-edge-fix-under-cgraph-edge-equiv

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

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

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

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

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

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

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

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

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