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• Matchmode

Matchmode-fix

Fixing function for matchmode structures.

Signature

(matchmode-fix x) → new-x

Arguments

x — Guard (matchmode-p x).

Returns

new-x — Type (matchmode-p new-x).

Definitions and Theorems

Function: matchmode-fix$inline

(defun matchmode-fix$inline (x)
  (declare (xargs :guard (matchmode-p x)))
  (let ((__function__ 'matchmode-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((case-insens (acl2::bool-fix x)))
           case-insens)
         :exec x)))

Theorem: matchmode-p-of-matchmode-fix

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

Theorem: matchmode-fix-when-matchmode-p

(defthm matchmode-fix-when-matchmode-p
  (implies (matchmode-p x)
           (equal (matchmode-fix x) x)))

Function: matchmode-equiv$inline

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

Theorem: matchmode-equiv-is-an-equivalence

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

Theorem: matchmode-equiv-implies-equal-matchmode-fix-1

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

Theorem: matchmode-fix-under-matchmode-equiv

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

Theorem: equal-of-matchmode-fix-1-forward-to-matchmode-equiv

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

Theorem: equal-of-matchmode-fix-2-forward-to-matchmode-equiv

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

Theorem: matchmode-equiv-of-matchmode-fix-1-forward

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

Theorem: matchmode-equiv-of-matchmode-fix-2-forward

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