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• Fgl-config

Fgl-config-fix

Fixing function for fgl-config structures.

Signature

(fgl-config-fix x) → new-x

Arguments

x — Guard (fgl-config-p x).

Returns

new-x — Type (fgl-config-p new-x).

Definitions and Theorems

Function: fgl-config-fix$inline

(defun fgl-config-fix$inline (x)
 (declare (xargs :guard (fgl-config-p x)))
 (let ((__function__ 'fgl-config-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((trace-rewrites
       (bool-fix (std::prod-car (std::prod-car (std::prod-car x)))))
     (reclimit
      (pos-fix
           (std::prod-car
                (std::prod-cdr (std::prod-car (std::prod-car x))))))
     (stacklimit
      (pos-fix
           (std::prod-cdr
                (std::prod-cdr (std::prod-car (std::prod-car x))))))
     (steplimit
      (pos-fix
           (std::prod-car
                (std::prod-car (std::prod-cdr (std::prod-car x))))))
     (make-ites
      (bool-fix
           (std::prod-cdr
                (std::prod-car (std::prod-cdr (std::prod-car x))))))
     (rewrite-rule-table
          (std::prod-car
               (std::prod-cdr (std::prod-cdr (std::prod-car x)))))
     (branch-merge-rules
          (std::prod-cdr
               (std::prod-cdr (std::prod-cdr (std::prod-car x)))))
     (function-modes
      (fgl-function-mode-alist-fix
           (std::prod-car
                (std::prod-car (std::prod-car (std::prod-cdr x))))))
     (counterexample-analysis-enabledp
      (bool-fix
           (std::prod-cdr
                (std::prod-car (std::prod-car (std::prod-cdr x))))))
     (prof-enabledp
      (bool-fix
           (std::prod-car
                (std::prod-cdr (std::prod-car (std::prod-cdr x))))))
     (sat-config
          (std::prod-cdr
               (std::prod-cdr (std::prod-car (std::prod-cdr x)))))
     (sat-config-vacuity
          (std::prod-car
               (std::prod-car (std::prod-cdr (std::prod-cdr x)))))
     (toplevel-sat-check
      (fgl-toplevel-sat-check-mode-fix
           (std::prod-cdr
                (std::prod-car (std::prod-cdr (std::prod-cdr x))))))
     (skip-vacuity-check
      (bool-fix
           (std::prod-car
                (std::prod-cdr (std::prod-cdr (std::prod-cdr x))))))
     (evisc-tuple
          (std::prod-cdr
               (std::prod-cdr (std::prod-cdr (std::prod-cdr x))))))
    (std::prod-cons
     (std::prod-cons
       (std::prod-cons trace-rewrites
                       (std::prod-cons reclimit stacklimit))
       (std::prod-cons
            (std::prod-cons steplimit make-ites)
            (std::prod-cons rewrite-rule-table branch-merge-rules)))
     (std::prod-cons
         (std::prod-cons
              (std::prod-cons function-modes
                              counterexample-analysis-enabledp)
              (std::prod-cons prof-enabledp sat-config))
         (std::prod-cons
              (std::prod-cons sat-config-vacuity toplevel-sat-check)
              (std::prod-cons skip-vacuity-check evisc-tuple)))))
   :exec x)))

Theorem: fgl-config-p-of-fgl-config-fix

(defthm fgl-config-p-of-fgl-config-fix
  (b* ((new-x (fgl-config-fix$inline x)))
    (fgl-config-p new-x))
  :rule-classes :rewrite)

Theorem: fgl-config-fix-when-fgl-config-p

(defthm fgl-config-fix-when-fgl-config-p
  (implies (fgl-config-p x)
           (equal (fgl-config-fix x) x)))

Function: fgl-config-equiv$inline

(defun fgl-config-equiv$inline (x y)
  (declare (xargs :guard (and (fgl-config-p x)
                              (fgl-config-p y))))
  (equal (fgl-config-fix x)
         (fgl-config-fix y)))

Theorem: fgl-config-equiv-is-an-equivalence

(defthm fgl-config-equiv-is-an-equivalence
  (and (booleanp (fgl-config-equiv x y))
       (fgl-config-equiv x x)
       (implies (fgl-config-equiv x y)
                (fgl-config-equiv y x))
       (implies (and (fgl-config-equiv x y)
                     (fgl-config-equiv y z))
                (fgl-config-equiv x z)))
  :rule-classes (:equivalence))

Theorem: fgl-config-equiv-implies-equal-fgl-config-fix-1

(defthm fgl-config-equiv-implies-equal-fgl-config-fix-1
  (implies (fgl-config-equiv x x-equiv)
           (equal (fgl-config-fix x)
                  (fgl-config-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: fgl-config-fix-under-fgl-config-equiv

(defthm fgl-config-fix-under-fgl-config-equiv
  (fgl-config-equiv (fgl-config-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-fgl-config-fix-1-forward-to-fgl-config-equiv

(defthm equal-of-fgl-config-fix-1-forward-to-fgl-config-equiv
  (implies (equal (fgl-config-fix x) y)
           (fgl-config-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-fgl-config-fix-2-forward-to-fgl-config-equiv

(defthm equal-of-fgl-config-fix-2-forward-to-fgl-config-equiv
  (implies (equal x (fgl-config-fix y))
           (fgl-config-equiv x y))
  :rule-classes :forward-chaining)

Theorem: fgl-config-equiv-of-fgl-config-fix-1-forward

(defthm fgl-config-equiv-of-fgl-config-fix-1-forward
  (implies (fgl-config-equiv (fgl-config-fix x) y)
           (fgl-config-equiv x y))
  :rule-classes :forward-chaining)

Theorem: fgl-config-equiv-of-fgl-config-fix-2-forward

(defthm fgl-config-equiv-of-fgl-config-fix-2-forward
  (implies (fgl-config-equiv x (fgl-config-fix y))
           (fgl-config-equiv x y))
  :rule-classes :forward-chaining)