Fixing function for run-snippet-file-info structures.
(run-snippet-file-info-fix x) → new-x
Function:
(defun run-snippet-file-info-fix$inline (x) (declare (xargs :guard (run-snippet-file-info-p x))) (let ((__function__ 'run-snippet-file-info-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((snip-info (run-snippet-info-fix (cdr (std::da-nth 0 x)))) (input-addr (canonical-address-fix (cdr (std::da-nth 1 x)))) (output-addr (canonical-address-fix (cdr (std::da-nth 2 x)))) (input-channel (acl2::symbol-fix (cdr (std::da-nth 3 x)))) (output-channel (acl2::symbol-fix (cdr (std::da-nth 4 x))))) (list (cons 'snip-info snip-info) (cons 'input-addr input-addr) (cons 'output-addr output-addr) (cons 'input-channel input-channel) (cons 'output-channel output-channel))) :exec x)))
Theorem:
(defthm run-snippet-file-info-p-of-run-snippet-file-info-fix (b* ((new-x (run-snippet-file-info-fix$inline x))) (run-snippet-file-info-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm run-snippet-file-info-fix-when-run-snippet-file-info-p (implies (run-snippet-file-info-p x) (equal (run-snippet-file-info-fix x) x)))
Function:
(defun run-snippet-file-info-equiv$inline (x y) (declare (xargs :guard (and (run-snippet-file-info-p x) (run-snippet-file-info-p y)))) (equal (run-snippet-file-info-fix x) (run-snippet-file-info-fix y)))
Theorem:
(defthm run-snippet-file-info-equiv-is-an-equivalence (and (booleanp (run-snippet-file-info-equiv x y)) (run-snippet-file-info-equiv x x) (implies (run-snippet-file-info-equiv x y) (run-snippet-file-info-equiv y x)) (implies (and (run-snippet-file-info-equiv x y) (run-snippet-file-info-equiv y z)) (run-snippet-file-info-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm run-snippet-file-info-equiv-implies-equal-run-snippet-file-info-fix-1 (implies (run-snippet-file-info-equiv x x-equiv) (equal (run-snippet-file-info-fix x) (run-snippet-file-info-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm run-snippet-file-info-fix-under-run-snippet-file-info-equiv (run-snippet-file-info-equiv (run-snippet-file-info-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-run-snippet-file-info-fix-1-forward-to-run-snippet-file-info-equiv (implies (equal (run-snippet-file-info-fix x) y) (run-snippet-file-info-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-run-snippet-file-info-fix-2-forward-to-run-snippet-file-info-equiv (implies (equal x (run-snippet-file-info-fix y)) (run-snippet-file-info-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm run-snippet-file-info-equiv-of-run-snippet-file-info-fix-1-forward (implies (run-snippet-file-info-equiv (run-snippet-file-info-fix x) y) (run-snippet-file-info-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm run-snippet-file-info-equiv-of-run-snippet-file-info-fix-2-forward (implies (run-snippet-file-info-equiv x (run-snippet-file-info-fix y)) (run-snippet-file-info-equiv x y)) :rule-classes :forward-chaining)