Fixing function for output-expression structures.
(output-expression-fix x) → new-x
Function:
(defun output-expression-fix$inline (x) (declare (xargs :guard (output-expressionp x))) (let ((__function__ 'output-expression-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((get (expression-fix (cdr (std::da-nth 0 (cdr x)))))) (cons :output-expression (list (cons 'get get)))) :exec x)))
Theorem:
(defthm output-expressionp-of-output-expression-fix (b* ((new-x (output-expression-fix$inline x))) (output-expressionp new-x)) :rule-classes :rewrite)
Theorem:
(defthm output-expression-fix-when-output-expressionp (implies (output-expressionp x) (equal (output-expression-fix x) x)))
Function:
(defun output-expression-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (output-expressionp acl2::x) (output-expressionp acl2::y)))) (equal (output-expression-fix acl2::x) (output-expression-fix acl2::y)))
Theorem:
(defthm output-expression-equiv-is-an-equivalence (and (booleanp (output-expression-equiv x y)) (output-expression-equiv x x) (implies (output-expression-equiv x y) (output-expression-equiv y x)) (implies (and (output-expression-equiv x y) (output-expression-equiv y z)) (output-expression-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm output-expression-equiv-implies-equal-output-expression-fix-1 (implies (output-expression-equiv acl2::x x-equiv) (equal (output-expression-fix acl2::x) (output-expression-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm output-expression-fix-under-output-expression-equiv (output-expression-equiv (output-expression-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-output-expression-fix-1-forward-to-output-expression-equiv (implies (equal (output-expression-fix acl2::x) acl2::y) (output-expression-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-output-expression-fix-2-forward-to-output-expression-equiv (implies (equal acl2::x (output-expression-fix acl2::y)) (output-expression-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm output-expression-equiv-of-output-expression-fix-1-forward (implies (output-expression-equiv (output-expression-fix acl2::x) acl2::y) (output-expression-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm output-expression-equiv-of-output-expression-fix-2-forward (implies (output-expression-equiv acl2::x (output-expression-fix acl2::y)) (output-expression-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)