Basic equivalence relation for declspec structures.
Function:
(defun declspec-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (declspecp acl2::x) (declspecp acl2::y)))) (equal (declspec-fix acl2::x) (declspec-fix acl2::y)))
Theorem:
(defthm declspec-equiv-is-an-equivalence (and (booleanp (declspec-equiv x y)) (declspec-equiv x x) (implies (declspec-equiv x y) (declspec-equiv y x)) (implies (and (declspec-equiv x y) (declspec-equiv y z)) (declspec-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm declspec-equiv-implies-equal-declspec-fix-1 (implies (declspec-equiv acl2::x x-equiv) (equal (declspec-fix acl2::x) (declspec-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm declspec-fix-under-declspec-equiv (declspec-equiv (declspec-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-declspec-fix-1-forward-to-declspec-equiv (implies (equal (declspec-fix acl2::x) acl2::y) (declspec-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-declspec-fix-2-forward-to-declspec-equiv (implies (equal acl2::x (declspec-fix acl2::y)) (declspec-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm declspec-equiv-of-declspec-fix-1-forward (implies (declspec-equiv (declspec-fix acl2::x) acl2::y) (declspec-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm declspec-equiv-of-declspec-fix-2-forward (implies (declspec-equiv acl2::x (declspec-fix acl2::y)) (declspec-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)