Fixing function for asm-name-spec structures.
(asm-name-spec-fix x) → new-x
Function:
(defun asm-name-spec-fix$inline (x) (declare (xargs :guard (asm-name-specp x))) (let ((__function__ 'asm-name-spec-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((strings (stringlit-list-fix (cdr (std::da-nth 0 x)))) (uscores (bool-fix (cdr (std::da-nth 1 x))))) (list (cons 'strings strings) (cons 'uscores uscores))) :exec x)))
Theorem:
(defthm asm-name-specp-of-asm-name-spec-fix (b* ((new-x (asm-name-spec-fix$inline x))) (asm-name-specp new-x)) :rule-classes :rewrite)
Theorem:
(defthm asm-name-spec-fix-when-asm-name-specp (implies (asm-name-specp x) (equal (asm-name-spec-fix x) x)))
Function:
(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:
(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:
(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:
(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:
(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:
(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:
(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:
(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)