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Asm-qual

Asm-qual-fix

Fixing function for asm-qual structures.

Signature
(asm-qual-fix x) → new-x
Arguments: x — Guard (asm-qualp x).
Returns: new-x — Type (asm-qualp new-x).

Definitions and Theorems

Function: asm-qual-fix$inline

(defun asm-qual-fix$inline (x)
  (declare (xargs :guard (asm-qualp x)))
  (mbe :logic
       (case (asm-qual-kind x)
         (:volatile (b* ((uscores (keyword-uscores-fix (cdr x))))
                      (cons :volatile uscores)))
         (:inline (b* ((uscores (keyword-uscores-fix (cdr x))))
                    (cons :inline uscores)))
         (:goto (cons :goto nil)))
       :exec x))

Theorem: asm-qualp-of-asm-qual-fix

(defthm asm-qualp-of-asm-qual-fix
  (b* ((new-x (asm-qual-fix$inline x)))
    (asm-qualp new-x))
  :rule-classes :rewrite)

Theorem: asm-qual-fix-when-asm-qualp

(defthm asm-qual-fix-when-asm-qualp
  (implies (asm-qualp x)
           (equal (asm-qual-fix x) x)))

Function: asm-qual-equiv$inline

(defun asm-qual-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (asm-qualp acl2::x)
                              (asm-qualp acl2::y))))
  (equal (asm-qual-fix acl2::x)
         (asm-qual-fix acl2::y)))

Theorem: asm-qual-equiv-is-an-equivalence

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

Theorem: asm-qual-equiv-implies-equal-asm-qual-fix-1

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

Theorem: asm-qual-fix-under-asm-qual-equiv

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

Theorem: equal-of-asm-qual-fix-1-forward-to-asm-qual-equiv

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

Theorem: equal-of-asm-qual-fix-2-forward-to-asm-qual-equiv

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

Theorem: asm-qual-equiv-of-asm-qual-fix-1-forward

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

Theorem: asm-qual-equiv-of-asm-qual-fix-2-forward

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

Theorem: asm-qual-kind$inline-of-asm-qual-fix-x

(defthm asm-qual-kind$inline-of-asm-qual-fix-x
  (equal (asm-qual-kind$inline (asm-qual-fix x))
         (asm-qual-kind$inline x)))

Theorem: asm-qual-kind$inline-asm-qual-equiv-congruence-on-x

(defthm asm-qual-kind$inline-asm-qual-equiv-congruence-on-x
  (implies (asm-qual-equiv x x-equiv)
           (equal (asm-qual-kind$inline x)
                  (asm-qual-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-asm-qual-fix

(defthm consp-of-asm-qual-fix
  (consp (asm-qual-fix x))
  :rule-classes :type-prescription)

Theorem: asm-qual-fix$inline-of-asm-qual-fix-x

(defthm asm-qual-fix$inline-of-asm-qual-fix-x
  (equal (asm-qual-fix$inline (asm-qual-fix x))
         (asm-qual-fix$inline x)))

Theorem: asm-qual-fix$inline-asm-qual-equiv-congruence-on-x

(defthm asm-qual-fix$inline-asm-qual-equiv-congruence-on-x
  (implies (asm-qual-equiv x x-equiv)
           (equal (asm-qual-fix$inline x)
                  (asm-qual-fix$inline x-equiv)))
  :rule-classes :congruence)