Fixing function for decl structures.
Function:
(defun decl-fix$inline (x) (declare (xargs :guard (declp x))) (let ((__function__ 'decl-fix)) (declare (ignorable __function__)) (mbe :logic (case (decl-kind x) (:decl (b* ((extension (bool-fix (std::da-nth 0 (cdr x)))) (specs (declspec-list-fix (std::da-nth 1 (cdr x)))) (init (initdeclor-list-fix (std::da-nth 2 (cdr x)))) (asm? (asm-name-spec-option-fix (std::da-nth 3 (cdr x)))) (attrib (attrib-spec-list-fix (std::da-nth 4 (cdr x))))) (cons :decl (list extension specs init asm? attrib)))) (:statassert (b* ((unwrap (statassert-fix (std::da-nth 0 (cdr x))))) (cons :statassert (list unwrap))))) :exec x)))
Theorem:
(defthm declp-of-decl-fix (b* ((new-x (decl-fix$inline x))) (declp new-x)) :rule-classes :rewrite)
Theorem:
(defthm decl-fix-when-declp (implies (declp x) (equal (decl-fix x) x)))
Function:
(defun decl-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (declp acl2::x) (declp acl2::y)))) (equal (decl-fix acl2::x) (decl-fix acl2::y)))
Theorem:
(defthm decl-equiv-is-an-equivalence (and (booleanp (decl-equiv x y)) (decl-equiv x x) (implies (decl-equiv x y) (decl-equiv y x)) (implies (and (decl-equiv x y) (decl-equiv y z)) (decl-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm decl-equiv-implies-equal-decl-fix-1 (implies (decl-equiv acl2::x x-equiv) (equal (decl-fix acl2::x) (decl-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm decl-fix-under-decl-equiv (decl-equiv (decl-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-decl-fix-1-forward-to-decl-equiv (implies (equal (decl-fix acl2::x) acl2::y) (decl-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-decl-fix-2-forward-to-decl-equiv (implies (equal acl2::x (decl-fix acl2::y)) (decl-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm decl-equiv-of-decl-fix-1-forward (implies (decl-equiv (decl-fix acl2::x) acl2::y) (decl-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm decl-equiv-of-decl-fix-2-forward (implies (decl-equiv acl2::x (decl-fix acl2::y)) (decl-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm decl-kind$inline-of-decl-fix-x (equal (decl-kind$inline (decl-fix x)) (decl-kind$inline x)))
Theorem:
(defthm decl-kind$inline-decl-equiv-congruence-on-x (implies (decl-equiv x x-equiv) (equal (decl-kind$inline x) (decl-kind$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm consp-of-decl-fix (consp (decl-fix x)) :rule-classes :type-prescription)