Fixing function for atc-var-info-option structures.
(atc-var-info-option-fix x) → new-x
Function:
(defun atc-var-info-option-fix$inline (x) (declare (xargs :guard (atc-var-info-optionp x))) (let ((__function__ 'atc-var-info-option-fix)) (declare (ignorable __function__)) (mbe :logic (cond ((not x) nil) (t (b* ((fty::val (atc-var-info-fix x))) fty::val))) :exec x)))
Theorem:
(defthm atc-var-info-optionp-of-atc-var-info-option-fix (b* ((new-x (atc-var-info-option-fix$inline x))) (atc-var-info-optionp new-x)) :rule-classes :rewrite)
Theorem:
(defthm atc-var-info-option-fix-when-atc-var-info-optionp (implies (atc-var-info-optionp x) (equal (atc-var-info-option-fix x) x)))
Function:
(defun atc-var-info-option-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (atc-var-info-optionp acl2::x) (atc-var-info-optionp acl2::y)))) (equal (atc-var-info-option-fix acl2::x) (atc-var-info-option-fix acl2::y)))
Theorem:
(defthm atc-var-info-option-equiv-is-an-equivalence (and (booleanp (atc-var-info-option-equiv x y)) (atc-var-info-option-equiv x x) (implies (atc-var-info-option-equiv x y) (atc-var-info-option-equiv y x)) (implies (and (atc-var-info-option-equiv x y) (atc-var-info-option-equiv y z)) (atc-var-info-option-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm atc-var-info-option-equiv-implies-equal-atc-var-info-option-fix-1 (implies (atc-var-info-option-equiv acl2::x x-equiv) (equal (atc-var-info-option-fix acl2::x) (atc-var-info-option-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm atc-var-info-option-fix-under-atc-var-info-option-equiv (atc-var-info-option-equiv (atc-var-info-option-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-atc-var-info-option-fix-1-forward-to-atc-var-info-option-equiv (implies (equal (atc-var-info-option-fix acl2::x) acl2::y) (atc-var-info-option-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-atc-var-info-option-fix-2-forward-to-atc-var-info-option-equiv (implies (equal acl2::x (atc-var-info-option-fix acl2::y)) (atc-var-info-option-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm atc-var-info-option-equiv-of-atc-var-info-option-fix-1-forward (implies (atc-var-info-option-equiv (atc-var-info-option-fix acl2::x) acl2::y) (atc-var-info-option-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm atc-var-info-option-equiv-of-atc-var-info-option-fix-2-forward (implies (atc-var-info-option-equiv acl2::x (atc-var-info-option-fix acl2::y)) (atc-var-info-option-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)