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• Fgl-env

Fgl-env-fix

Fixing function for fgl-env structures.

Signature

(fgl-env-fix x) → new-x

Arguments

x — Guard (fgl-env-p x).

Returns

new-x — Type (fgl-env-p new-x).

Definitions and Theorems

Function: fgl-env-fix$inline

(defun fgl-env-fix$inline (x)
  (declare (xargs :guard (fgl-env-p x)))
  (let ((__function__ 'fgl-env-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((obj-alist (obj-alist-fix (std::prod-car x)))
              (bfr-vals (std::prod-cdr x)))
           (std::prod-cons obj-alist bfr-vals))
         :exec x)))

Theorem: fgl-env-p-of-fgl-env-fix

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

Theorem: fgl-env-fix-when-fgl-env-p

(defthm fgl-env-fix-when-fgl-env-p
  (implies (fgl-env-p x)
           (equal (fgl-env-fix x) x)))

Function: fgl-env-equiv$inline

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

Theorem: fgl-env-equiv-is-an-equivalence

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

Theorem: fgl-env-equiv-implies-equal-fgl-env-fix-1

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

Theorem: fgl-env-fix-under-fgl-env-equiv

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

Theorem: equal-of-fgl-env-fix-1-forward-to-fgl-env-equiv

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

Theorem: equal-of-fgl-env-fix-2-forward-to-fgl-env-equiv

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

Theorem: fgl-env-equiv-of-fgl-env-fix-1-forward

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

Theorem: fgl-env-equiv-of-fgl-env-fix-2-forward

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