Fixing function for expr-priority structures.
(expr-priority-fix x) → new-x
Function:
(defun expr-priority-fix$inline (x) (declare (xargs :guard (expr-priorityp x))) (let ((__function__ 'expr-priority-fix)) (declare (ignorable __function__)) (mbe :logic (case (expr-priority-kind x) (:primary (cons :primary (list))) (:postfix (cons :postfix (list))) (:unary (cons :unary (list))) (:cast (cons :cast (list))) (:mul (cons :mul (list))) (:add (cons :add (list))) (:sh (cons :sh (list))) (:rel (cons :rel (list))) (:eq (cons :eq (list))) (:and (cons :and (list))) (:xor (cons :xor (list))) (:ior (cons :ior (list))) (:logand (cons :logand (list))) (:logor (cons :logor (list))) (:cond (cons :cond (list))) (:asg (cons :asg (list))) (:expr (cons :expr (list)))) :exec x)))
Theorem:
(defthm expr-priorityp-of-expr-priority-fix (b* ((new-x (expr-priority-fix$inline x))) (expr-priorityp new-x)) :rule-classes :rewrite)
Theorem:
(defthm expr-priority-fix-when-expr-priorityp (implies (expr-priorityp x) (equal (expr-priority-fix x) x)))
Function:
(defun expr-priority-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (expr-priorityp acl2::x) (expr-priorityp acl2::y)))) (equal (expr-priority-fix acl2::x) (expr-priority-fix acl2::y)))
Theorem:
(defthm expr-priority-equiv-is-an-equivalence (and (booleanp (expr-priority-equiv x y)) (expr-priority-equiv x x) (implies (expr-priority-equiv x y) (expr-priority-equiv y x)) (implies (and (expr-priority-equiv x y) (expr-priority-equiv y z)) (expr-priority-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm expr-priority-equiv-implies-equal-expr-priority-fix-1 (implies (expr-priority-equiv acl2::x x-equiv) (equal (expr-priority-fix acl2::x) (expr-priority-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm expr-priority-fix-under-expr-priority-equiv (expr-priority-equiv (expr-priority-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-expr-priority-fix-1-forward-to-expr-priority-equiv (implies (equal (expr-priority-fix acl2::x) acl2::y) (expr-priority-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-expr-priority-fix-2-forward-to-expr-priority-equiv (implies (equal acl2::x (expr-priority-fix acl2::y)) (expr-priority-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm expr-priority-equiv-of-expr-priority-fix-1-forward (implies (expr-priority-equiv (expr-priority-fix acl2::x) acl2::y) (expr-priority-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm expr-priority-equiv-of-expr-priority-fix-2-forward (implies (expr-priority-equiv acl2::x (expr-priority-fix acl2::y)) (expr-priority-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm expr-priority-kind$inline-of-expr-priority-fix-x (equal (expr-priority-kind$inline (expr-priority-fix x)) (expr-priority-kind$inline x)))
Theorem:
(defthm expr-priority-kind$inline-expr-priority-equiv-congruence-on-x (implies (expr-priority-equiv x x-equiv) (equal (expr-priority-kind$inline x) (expr-priority-kind$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm consp-of-expr-priority-fix (consp (expr-priority-fix x)) :rule-classes :type-prescription)