Fixing function for vl-parsed-portdecl-head structures.
(vl-parsed-portdecl-head-fix x) → new-x
Function:
(defun vl-parsed-portdecl-head-fix$inline (x) (declare (xargs :guard (vl-parsed-portdecl-head-p x))) (let ((__function__ 'vl-parsed-portdecl-head-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((nettype (vl-maybe-nettypename-fix (std::prod-car (std::prod-car (cdr x))))) (var-p (acl2::bool-fix (std::prod-cdr (std::prod-car (cdr x))))) (explicit-p (acl2::bool-fix (std::prod-car (std::prod-cdr (cdr x))))) (implicit-p (acl2::bool-fix (std::prod-car (std::prod-cdr (std::prod-cdr (cdr x)))))) (type (vl-datatype-fix (std::prod-cdr (std::prod-cdr (std::prod-cdr (cdr x))))))) (cons :vl-parsed-portdecl-head (std::prod-cons (std::prod-cons nettype var-p) (std::prod-cons explicit-p (std::prod-cons implicit-p type))))) :exec x)))
Theorem:
(defthm vl-parsed-portdecl-head-p-of-vl-parsed-portdecl-head-fix (b* ((new-x (vl-parsed-portdecl-head-fix$inline x))) (vl-parsed-portdecl-head-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm vl-parsed-portdecl-head-fix-when-vl-parsed-portdecl-head-p (implies (vl-parsed-portdecl-head-p x) (equal (vl-parsed-portdecl-head-fix x) x)))
Function:
(defun vl-parsed-portdecl-head-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (vl-parsed-portdecl-head-p acl2::x) (vl-parsed-portdecl-head-p acl2::y)))) (equal (vl-parsed-portdecl-head-fix acl2::x) (vl-parsed-portdecl-head-fix acl2::y)))
Theorem:
(defthm vl-parsed-portdecl-head-equiv-is-an-equivalence (and (booleanp (vl-parsed-portdecl-head-equiv x y)) (vl-parsed-portdecl-head-equiv x x) (implies (vl-parsed-portdecl-head-equiv x y) (vl-parsed-portdecl-head-equiv y x)) (implies (and (vl-parsed-portdecl-head-equiv x y) (vl-parsed-portdecl-head-equiv y z)) (vl-parsed-portdecl-head-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm vl-parsed-portdecl-head-equiv-implies-equal-vl-parsed-portdecl-head-fix-1 (implies (vl-parsed-portdecl-head-equiv acl2::x x-equiv) (equal (vl-parsed-portdecl-head-fix acl2::x) (vl-parsed-portdecl-head-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm vl-parsed-portdecl-head-fix-under-vl-parsed-portdecl-head-equiv (vl-parsed-portdecl-head-equiv (vl-parsed-portdecl-head-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-vl-parsed-portdecl-head-fix-1-forward-to-vl-parsed-portdecl-head-equiv (implies (equal (vl-parsed-portdecl-head-fix acl2::x) acl2::y) (vl-parsed-portdecl-head-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-vl-parsed-portdecl-head-fix-2-forward-to-vl-parsed-portdecl-head-equiv (implies (equal acl2::x (vl-parsed-portdecl-head-fix acl2::y)) (vl-parsed-portdecl-head-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm vl-parsed-portdecl-head-equiv-of-vl-parsed-portdecl-head-fix-1-forward (implies (vl-parsed-portdecl-head-equiv (vl-parsed-portdecl-head-fix acl2::x) acl2::y) (vl-parsed-portdecl-head-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm vl-parsed-portdecl-head-equiv-of-vl-parsed-portdecl-head-fix-2-forward (implies (vl-parsed-portdecl-head-equiv acl2::x (vl-parsed-portdecl-head-fix acl2::y)) (vl-parsed-portdecl-head-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)