Fixing function for ctrex-rule structures.
(ctrex-rule-fix x) → new-x
Function:
(defun ctrex-rule-fix$inline (x) (declare (xargs :guard (ctrex-rule-p x))) (let ((__function__ 'ctrex-rule-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((name (acl2::symbol-fix (cdr (std::da-nth 0 x)))) (match (pseudo-term-fix (cdr (std::da-nth 1 x)))) (unify-subst (fgl-object-bindings-fix (cdr (std::da-nth 2 x)))) (target (pseudo-term-fix (cdr (std::da-nth 3 x)))) (deps (pseudo-term-subst-fix (cdr (std::da-nth 4 x)))) (dep-success-vars (pseudo-term-subst-fix (cdr (std::da-nth 5 x)))) (success (pseudo-term-fix (cdr (std::da-nth 6 x)))) (priority (pseudo-term-fix (cdr (std::da-nth 7 x)))) (value (pseudo-term-fix (cdr (std::da-nth 8 x)))) (order (nfix (cdr (std::da-nth 9 x)))) (ruletype (ctrex-ruletype-fix (cdr (std::da-nth 10 x))))) (list (cons 'name name) (cons 'match match) (cons 'unify-subst unify-subst) (cons 'target target) (cons 'deps deps) (cons 'dep-success-vars dep-success-vars) (cons 'success success) (cons 'priority priority) (cons 'value value) (cons 'order order) (cons 'ruletype ruletype))) :exec x)))
Theorem:
(defthm ctrex-rule-p-of-ctrex-rule-fix (b* ((new-x (ctrex-rule-fix$inline x))) (ctrex-rule-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm ctrex-rule-fix-when-ctrex-rule-p (implies (ctrex-rule-p x) (equal (ctrex-rule-fix x) x)))
Function:
(defun ctrex-rule-equiv$inline (x y) (declare (xargs :guard (and (ctrex-rule-p x) (ctrex-rule-p y)))) (equal (ctrex-rule-fix x) (ctrex-rule-fix y)))
Theorem:
(defthm ctrex-rule-equiv-is-an-equivalence (and (booleanp (ctrex-rule-equiv x y)) (ctrex-rule-equiv x x) (implies (ctrex-rule-equiv x y) (ctrex-rule-equiv y x)) (implies (and (ctrex-rule-equiv x y) (ctrex-rule-equiv y z)) (ctrex-rule-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm ctrex-rule-equiv-implies-equal-ctrex-rule-fix-1 (implies (ctrex-rule-equiv x x-equiv) (equal (ctrex-rule-fix x) (ctrex-rule-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm ctrex-rule-fix-under-ctrex-rule-equiv (ctrex-rule-equiv (ctrex-rule-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-ctrex-rule-fix-1-forward-to-ctrex-rule-equiv (implies (equal (ctrex-rule-fix x) y) (ctrex-rule-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-ctrex-rule-fix-2-forward-to-ctrex-rule-equiv (implies (equal x (ctrex-rule-fix y)) (ctrex-rule-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm ctrex-rule-equiv-of-ctrex-rule-fix-1-forward (implies (ctrex-rule-equiv (ctrex-rule-fix x) y) (ctrex-rule-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm ctrex-rule-equiv-of-ctrex-rule-fix-2-forward (implies (ctrex-rule-equiv x (ctrex-rule-fix y)) (ctrex-rule-equiv x y)) :rule-classes :forward-chaining)