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• Assertion

Assertion-fix

Fixing function for assertion structures.

Signature

(assertion-fix x) → new-x

Arguments

x — Guard (assertionp x).

Returns

new-x — Type (assertionp new-x).

Definitions and Theorems

Function: assertion-fix$inline

(defun assertion-fix$inline (x)
  (declare (xargs :guard (assertionp x)))
  (let ((__function__ 'assertion-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((asg (assignment-fix (cdr (std::da-nth 0 x))))
              (constr (constraint-fix (cdr (std::da-nth 1 x)))))
           (list (cons 'asg asg)
                 (cons 'constr constr)))
         :exec x)))

Theorem: assertionp-of-assertion-fix

(defthm assertionp-of-assertion-fix
  (b* ((new-x (assertion-fix$inline x)))
    (assertionp new-x))
  :rule-classes :rewrite)

Theorem: assertion-fix-when-assertionp

(defthm assertion-fix-when-assertionp
  (implies (assertionp x)
           (equal (assertion-fix x) x)))

Function: assertion-equiv$inline

(defun assertion-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (assertionp acl2::x)
                              (assertionp acl2::y))))
  (equal (assertion-fix acl2::x)
         (assertion-fix acl2::y)))

Theorem: assertion-equiv-is-an-equivalence

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

Theorem: assertion-equiv-implies-equal-assertion-fix-1

(defthm assertion-equiv-implies-equal-assertion-fix-1
  (implies (assertion-equiv acl2::x x-equiv)
           (equal (assertion-fix acl2::x)
                  (assertion-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: assertion-fix-under-assertion-equiv

(defthm assertion-fix-under-assertion-equiv
  (assertion-equiv (assertion-fix acl2::x)
                   acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-assertion-fix-1-forward-to-assertion-equiv

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

Theorem: equal-of-assertion-fix-2-forward-to-assertion-equiv

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

Theorem: assertion-equiv-of-assertion-fix-1-forward

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

Theorem: assertion-equiv-of-assertion-fix-2-forward

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