Fixing function for fgl-casesplit-config structures.
(fgl-casesplit-config-fix x) → new-x
Function:
(defun fgl-casesplit-config-fix$inline (x) (declare (xargs :guard (fgl-casesplit-config-p x))) (let ((__function__ 'fgl-casesplit-config-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((split-params (cdr (std::da-nth 0 x))) (solve-params (cdr (std::da-nth 1 x))) (split-concl (cdr (std::da-nth 2 x))) (repeat-concl (cdr (std::da-nth 3 x))) (allow-irrel-casesplit-vars (cdr (std::da-nth 4 x))) (cases (casesplit-alist-fix (cdr (std::da-nth 5 x)))) (fgl-config (fgl-config-fix (cdr (std::da-nth 6 x)))) (stop-on-ctrex (cdr (std::da-nth 7 x))) (stop-on-fail (cdr (std::da-nth 8 x)))) (list (cons 'split-params split-params) (cons 'solve-params solve-params) (cons 'split-concl split-concl) (cons 'repeat-concl repeat-concl) (cons 'allow-irrel-casesplit-vars allow-irrel-casesplit-vars) (cons 'cases cases) (cons 'fgl-config fgl-config) (cons 'stop-on-ctrex stop-on-ctrex) (cons 'stop-on-fail stop-on-fail))) :exec x)))
Theorem:
(defthm fgl-casesplit-config-p-of-fgl-casesplit-config-fix (b* ((new-x (fgl-casesplit-config-fix$inline x))) (fgl-casesplit-config-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm fgl-casesplit-config-fix-when-fgl-casesplit-config-p (implies (fgl-casesplit-config-p x) (equal (fgl-casesplit-config-fix x) x)))
Function:
(defun fgl-casesplit-config-equiv$inline (x y) (declare (xargs :guard (and (fgl-casesplit-config-p x) (fgl-casesplit-config-p y)))) (equal (fgl-casesplit-config-fix x) (fgl-casesplit-config-fix y)))
Theorem:
(defthm fgl-casesplit-config-equiv-is-an-equivalence (and (booleanp (fgl-casesplit-config-equiv x y)) (fgl-casesplit-config-equiv x x) (implies (fgl-casesplit-config-equiv x y) (fgl-casesplit-config-equiv y x)) (implies (and (fgl-casesplit-config-equiv x y) (fgl-casesplit-config-equiv y z)) (fgl-casesplit-config-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm fgl-casesplit-config-equiv-implies-equal-fgl-casesplit-config-fix-1 (implies (fgl-casesplit-config-equiv x x-equiv) (equal (fgl-casesplit-config-fix x) (fgl-casesplit-config-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm fgl-casesplit-config-fix-under-fgl-casesplit-config-equiv (fgl-casesplit-config-equiv (fgl-casesplit-config-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-fgl-casesplit-config-fix-1-forward-to-fgl-casesplit-config-equiv (implies (equal (fgl-casesplit-config-fix x) y) (fgl-casesplit-config-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-fgl-casesplit-config-fix-2-forward-to-fgl-casesplit-config-equiv (implies (equal x (fgl-casesplit-config-fix y)) (fgl-casesplit-config-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm fgl-casesplit-config-equiv-of-fgl-casesplit-config-fix-1-forward (implies (fgl-casesplit-config-equiv (fgl-casesplit-config-fix x) y) (fgl-casesplit-config-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm fgl-casesplit-config-equiv-of-fgl-casesplit-config-fix-2-forward (implies (fgl-casesplit-config-equiv x (fgl-casesplit-config-fix y)) (fgl-casesplit-config-equiv x y)) :rule-classes :forward-chaining)