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• Asm-name-spec

Asm-name-spec-fix

Fixing function for asm-name-spec structures.

Signature

(asm-name-spec-fix x) → new-x

Arguments

x — Guard (asm-name-specp x).

Returns

new-x — Type (asm-name-specp new-x).

Definitions and Theorems

Function: asm-name-spec-fix$inline

(defun asm-name-spec-fix$inline (x)
 (declare (xargs :guard (asm-name-specp x)))
 (let ((__function__ 'asm-name-spec-fix))
  (declare (ignorable __function__))
  (mbe :logic
       (b* ((strings (stringlit-list-fix (cdr (std::da-nth 0 x))))
            (uscores (keyword-uscores-fix (cdr (std::da-nth 1 x)))))
         (list (cons 'strings strings)
               (cons 'uscores uscores)))
       :exec x)))

Theorem: asm-name-specp-of-asm-name-spec-fix

(defthm asm-name-specp-of-asm-name-spec-fix
  (b* ((new-x (asm-name-spec-fix$inline x)))
    (asm-name-specp new-x))
  :rule-classes :rewrite)

Theorem: asm-name-spec-fix-when-asm-name-specp

(defthm asm-name-spec-fix-when-asm-name-specp
  (implies (asm-name-specp x)
           (equal (asm-name-spec-fix x) x)))

Function: asm-name-spec-equiv$inline

(defun asm-name-spec-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (asm-name-specp acl2::x)
                              (asm-name-specp acl2::y))))
  (equal (asm-name-spec-fix acl2::x)
         (asm-name-spec-fix acl2::y)))

Theorem: asm-name-spec-equiv-is-an-equivalence

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

Theorem: asm-name-spec-equiv-implies-equal-asm-name-spec-fix-1

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

Theorem: asm-name-spec-fix-under-asm-name-spec-equiv

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

Theorem: equal-of-asm-name-spec-fix-1-forward-to-asm-name-spec-equiv

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

Theorem: equal-of-asm-name-spec-fix-2-forward-to-asm-name-spec-equiv

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

Theorem: asm-name-spec-equiv-of-asm-name-spec-fix-1-forward

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

Theorem: asm-name-spec-equiv-of-asm-name-spec-fix-2-forward

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