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Satlink-parser-state

Satlink-parser-state-fix

Fixing function for satlink-parser-state structures.

Signature
(satlink-parser-state-fix x) → new-x
Arguments: x — Guard (satlink-parser-state-p x).
Returns: new-x — Type (satlink-parser-state-p new-x).

Definitions and Theorems

Function: satlink-parser-state-fix$inline

(defun satlink-parser-state-fix$inline (x)
 (declare (xargs :guard (satlink-parser-state-p x)))
 (let ((__function__ 'satlink-parser-state-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (b*
     ((saw-unsat-p
           (acl2::bool-fix (std::prod-car (std::prod-car x))))
      (saw-sat-p (acl2::bool-fix (std::prod-cdr (std::prod-car x))))
      (saw-unknown-p
           (acl2::bool-fix (std::prod-car (std::prod-cdr x))))
      (saw-zero-p
           (acl2::bool-fix (std::prod-cdr (std::prod-cdr x)))))
     (std::prod-cons (std::prod-cons saw-unsat-p saw-sat-p)
                     (std::prod-cons saw-unknown-p saw-zero-p)))
    :exec x)))

Theorem: satlink-parser-state-p-of-satlink-parser-state-fix

(defthm satlink-parser-state-p-of-satlink-parser-state-fix
  (b* ((new-x (satlink-parser-state-fix$inline x)))
    (satlink-parser-state-p new-x))
  :rule-classes :rewrite)

Theorem: satlink-parser-state-fix-when-satlink-parser-state-p

(defthm satlink-parser-state-fix-when-satlink-parser-state-p
  (implies (satlink-parser-state-p x)
           (equal (satlink-parser-state-fix x) x)))

Function: satlink-parser-state-equiv$inline

(defun satlink-parser-state-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (satlink-parser-state-p acl2::x)
                              (satlink-parser-state-p acl2::y))))
  (equal (satlink-parser-state-fix acl2::x)
         (satlink-parser-state-fix acl2::y)))

Theorem: satlink-parser-state-equiv-is-an-equivalence

(defthm satlink-parser-state-equiv-is-an-equivalence
  (and (booleanp (satlink-parser-state-equiv x y))
       (satlink-parser-state-equiv x x)
       (implies (satlink-parser-state-equiv x y)
                (satlink-parser-state-equiv y x))
       (implies (and (satlink-parser-state-equiv x y)
                     (satlink-parser-state-equiv y z))
                (satlink-parser-state-equiv x z)))
  :rule-classes (:equivalence))

Theorem: satlink-parser-state-equiv-implies-equal-satlink-parser-state-fix-1

(defthm
 satlink-parser-state-equiv-implies-equal-satlink-parser-state-fix-1
 (implies (satlink-parser-state-equiv acl2::x x-equiv)
          (equal (satlink-parser-state-fix acl2::x)
                 (satlink-parser-state-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: satlink-parser-state-fix-under-satlink-parser-state-equiv

(defthm satlink-parser-state-fix-under-satlink-parser-state-equiv
  (satlink-parser-state-equiv (satlink-parser-state-fix acl2::x)
                              acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-satlink-parser-state-fix-1-forward-to-satlink-parser-state-equiv

(defthm
 equal-of-satlink-parser-state-fix-1-forward-to-satlink-parser-state-equiv
 (implies (equal (satlink-parser-state-fix acl2::x)
                 acl2::y)
          (satlink-parser-state-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-satlink-parser-state-fix-2-forward-to-satlink-parser-state-equiv

(defthm
 equal-of-satlink-parser-state-fix-2-forward-to-satlink-parser-state-equiv
 (implies (equal acl2::x
                 (satlink-parser-state-fix acl2::y))
          (satlink-parser-state-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: satlink-parser-state-equiv-of-satlink-parser-state-fix-1-forward

(defthm
   satlink-parser-state-equiv-of-satlink-parser-state-fix-1-forward
 (implies
      (satlink-parser-state-equiv (satlink-parser-state-fix acl2::x)
                                  acl2::y)
      (satlink-parser-state-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: satlink-parser-state-equiv-of-satlink-parser-state-fix-2-forward

(defthm
   satlink-parser-state-equiv-of-satlink-parser-state-fix-2-forward
 (implies
     (satlink-parser-state-equiv acl2::x
                                 (satlink-parser-state-fix acl2::y))
     (satlink-parser-state-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)