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• Vl-bindelim-institem

Vl-bindelim-institem-fix

Fixing function for vl-bindelim-institem structures.

Signature

(vl-bindelim-institem-fix x) → new-x

Arguments

x — Guard (vl-bindelim-institem-p x).

Returns

new-x — Type (vl-bindelim-institem-p new-x).

Definitions and Theorems

Function: vl-bindelim-institem-fix$inline

(defun vl-bindelim-institem-fix$inline (x)
 (declare (xargs :guard (vl-bindelim-institem-p x)))
 (let ((__function__ 'vl-bindelim-institem-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (b*
      ((inst (vl-modinst-fix (std::prod-car (std::prod-car x))))
       (genp (acl2::bool-fix (std::prod-cdr (std::prod-car x))))
       (bindp (acl2::bool-fix (std::prod-car (std::prod-cdr x))))
       (ctx (vl-bindcontext-fix (std::prod-cdr (std::prod-cdr x)))))
      (std::prod-cons (std::prod-cons inst genp)
                      (std::prod-cons bindp ctx)))
    :exec x)))

Theorem: vl-bindelim-institem-p-of-vl-bindelim-institem-fix

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

Theorem: vl-bindelim-institem-fix-when-vl-bindelim-institem-p

(defthm vl-bindelim-institem-fix-when-vl-bindelim-institem-p
  (implies (vl-bindelim-institem-p x)
           (equal (vl-bindelim-institem-fix x) x)))

Function: vl-bindelim-institem-equiv$inline

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

Theorem: vl-bindelim-institem-equiv-is-an-equivalence

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

Theorem: vl-bindelim-institem-equiv-implies-equal-vl-bindelim-institem-fix-1

(defthm
 vl-bindelim-institem-equiv-implies-equal-vl-bindelim-institem-fix-1
 (implies (vl-bindelim-institem-equiv acl2::x x-equiv)
          (equal (vl-bindelim-institem-fix acl2::x)
                 (vl-bindelim-institem-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: vl-bindelim-institem-fix-under-vl-bindelim-institem-equiv

(defthm vl-bindelim-institem-fix-under-vl-bindelim-institem-equiv
  (vl-bindelim-institem-equiv (vl-bindelim-institem-fix acl2::x)
                              acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-vl-bindelim-institem-fix-1-forward-to-vl-bindelim-institem-equiv

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

Theorem: equal-of-vl-bindelim-institem-fix-2-forward-to-vl-bindelim-institem-equiv

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

Theorem: vl-bindelim-institem-equiv-of-vl-bindelim-institem-fix-1-forward

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

Theorem: vl-bindelim-institem-equiv-of-vl-bindelim-institem-fix-2-forward

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