Fixing function for fgl-ipasir-config structures.
(fgl-ipasir-config-fix x) → new-x
Function:
(defun fgl-ipasir-config-fix$inline (x) (declare (xargs :guard (fgl-ipasir-config-p x))) (let ((__function__ 'fgl-ipasir-config-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((ignore-pathcond (bool-fix (cdr (std::da-nth 0 (cdr x))))) (ignore-constraint (bool-fix (cdr (std::da-nth 1 (cdr x))))) (ipasir-callback-limit (acl2::maybe-natp-fix (cdr (std::da-nth 2 (cdr x))))) (ipasir-recycle-callback-limit (acl2::maybe-natp-fix (cdr (std::da-nth 3 (cdr x))))) (ipasir-index (nfix (cdr (std::da-nth 4 (cdr x)))))) (cons :fgl-ipasir-config (list (cons 'ignore-pathcond ignore-pathcond) (cons 'ignore-constraint ignore-constraint) (cons 'ipasir-callback-limit ipasir-callback-limit) (cons 'ipasir-recycle-callback-limit ipasir-recycle-callback-limit) (cons 'ipasir-index ipasir-index)))) :exec x)))
Theorem:
(defthm fgl-ipasir-config-p-of-fgl-ipasir-config-fix (b* ((new-x (fgl-ipasir-config-fix$inline x))) (fgl-ipasir-config-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm fgl-ipasir-config-fix-when-fgl-ipasir-config-p (implies (fgl-ipasir-config-p x) (equal (fgl-ipasir-config-fix x) x)))
Function:
(defun fgl-ipasir-config-equiv$inline (x y) (declare (xargs :guard (and (fgl-ipasir-config-p x) (fgl-ipasir-config-p y)))) (equal (fgl-ipasir-config-fix x) (fgl-ipasir-config-fix y)))
Theorem:
(defthm fgl-ipasir-config-equiv-is-an-equivalence (and (booleanp (fgl-ipasir-config-equiv x y)) (fgl-ipasir-config-equiv x x) (implies (fgl-ipasir-config-equiv x y) (fgl-ipasir-config-equiv y x)) (implies (and (fgl-ipasir-config-equiv x y) (fgl-ipasir-config-equiv y z)) (fgl-ipasir-config-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm fgl-ipasir-config-equiv-implies-equal-fgl-ipasir-config-fix-1 (implies (fgl-ipasir-config-equiv x x-equiv) (equal (fgl-ipasir-config-fix x) (fgl-ipasir-config-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm fgl-ipasir-config-fix-under-fgl-ipasir-config-equiv (fgl-ipasir-config-equiv (fgl-ipasir-config-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-fgl-ipasir-config-fix-1-forward-to-fgl-ipasir-config-equiv (implies (equal (fgl-ipasir-config-fix x) y) (fgl-ipasir-config-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-fgl-ipasir-config-fix-2-forward-to-fgl-ipasir-config-equiv (implies (equal x (fgl-ipasir-config-fix y)) (fgl-ipasir-config-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm fgl-ipasir-config-equiv-of-fgl-ipasir-config-fix-1-forward (implies (fgl-ipasir-config-equiv (fgl-ipasir-config-fix x) y) (fgl-ipasir-config-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm fgl-ipasir-config-equiv-of-fgl-ipasir-config-fix-2-forward (implies (fgl-ipasir-config-equiv x (fgl-ipasir-config-fix y)) (fgl-ipasir-config-equiv x y)) :rule-classes :forward-chaining)