Fixing function for decl/stmt structures.
(decl/stmt-fix x) → new-x
Function:
(defun decl/stmt-fix$inline (x) (declare (xargs :guard (decl/stmt-p x))) (let ((__function__ 'decl/stmt-fix)) (declare (ignorable __function__)) (mbe :logic (case (decl/stmt-kind x) (:decl (b* ((unwrap (decl-fix (std::da-nth 0 (cdr x))))) (cons :decl (list unwrap)))) (:stmt (b* ((unwrap (expr-fix (std::da-nth 0 (cdr x))))) (cons :stmt (list unwrap))))) :exec x)))
Theorem:
(defthm decl/stmt-p-of-decl/stmt-fix (b* ((new-x (decl/stmt-fix$inline x))) (decl/stmt-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm decl/stmt-fix-when-decl/stmt-p (implies (decl/stmt-p x) (equal (decl/stmt-fix x) x)))
Function:
(defun decl/stmt-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (decl/stmt-p acl2::x) (decl/stmt-p acl2::y)))) (equal (decl/stmt-fix acl2::x) (decl/stmt-fix acl2::y)))
Theorem:
(defthm decl/stmt-equiv-is-an-equivalence (and (booleanp (decl/stmt-equiv x y)) (decl/stmt-equiv x x) (implies (decl/stmt-equiv x y) (decl/stmt-equiv y x)) (implies (and (decl/stmt-equiv x y) (decl/stmt-equiv y z)) (decl/stmt-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm decl/stmt-equiv-implies-equal-decl/stmt-fix-1 (implies (decl/stmt-equiv acl2::x x-equiv) (equal (decl/stmt-fix acl2::x) (decl/stmt-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm decl/stmt-fix-under-decl/stmt-equiv (decl/stmt-equiv (decl/stmt-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-decl/stmt-fix-1-forward-to-decl/stmt-equiv (implies (equal (decl/stmt-fix acl2::x) acl2::y) (decl/stmt-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-decl/stmt-fix-2-forward-to-decl/stmt-equiv (implies (equal acl2::x (decl/stmt-fix acl2::y)) (decl/stmt-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm decl/stmt-equiv-of-decl/stmt-fix-1-forward (implies (decl/stmt-equiv (decl/stmt-fix acl2::x) acl2::y) (decl/stmt-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm decl/stmt-equiv-of-decl/stmt-fix-2-forward (implies (decl/stmt-equiv acl2::x (decl/stmt-fix acl2::y)) (decl/stmt-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm decl/stmt-kind$inline-of-decl/stmt-fix-x (equal (decl/stmt-kind$inline (decl/stmt-fix x)) (decl/stmt-kind$inline x)))
Theorem:
(defthm decl/stmt-kind$inline-decl/stmt-equiv-congruence-on-x (implies (decl/stmt-equiv x x-equiv) (equal (decl/stmt-kind$inline x) (decl/stmt-kind$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm consp-of-decl/stmt-fix (consp (decl/stmt-fix x)) :rule-classes :type-prescription)