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Obligation-hyp

Obligation-hyp-fix

Fixing function for obligation-hyp structures.

Signature
(obligation-hyp-fix x) → new-x
Arguments: x — Guard (obligation-hypp x).
Returns: new-x — Type (obligation-hypp new-x).

Definitions and Theorems

Function: obligation-hyp-fix$inline

(defun obligation-hyp-fix$inline (x)
 (declare (xargs :guard (obligation-hypp x)))
 (let ((__function__ 'obligation-hyp-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (obligation-hyp-kind x)
    (:condition (b* ((get (expression-fix (std::da-nth 0 (cdr x)))))
                  (cons :condition (list get))))
    (:binding (b* ((get (binding-fix (std::da-nth 0 (cdr x)))))
                (cons :binding (list get)))))
   :exec x)))

Theorem: obligation-hypp-of-obligation-hyp-fix

(defthm obligation-hypp-of-obligation-hyp-fix
  (b* ((new-x (obligation-hyp-fix$inline x)))
    (obligation-hypp new-x))
  :rule-classes :rewrite)

Theorem: obligation-hyp-fix-when-obligation-hypp

(defthm obligation-hyp-fix-when-obligation-hypp
  (implies (obligation-hypp x)
           (equal (obligation-hyp-fix x) x)))

Function: obligation-hyp-equiv$inline

(defun obligation-hyp-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (obligation-hypp acl2::x)
                              (obligation-hypp acl2::y))))
  (equal (obligation-hyp-fix acl2::x)
         (obligation-hyp-fix acl2::y)))

Theorem: obligation-hyp-equiv-is-an-equivalence

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

Theorem: obligation-hyp-equiv-implies-equal-obligation-hyp-fix-1

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

Theorem: obligation-hyp-fix-under-obligation-hyp-equiv

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

Theorem: equal-of-obligation-hyp-fix-1-forward-to-obligation-hyp-equiv

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

Theorem: equal-of-obligation-hyp-fix-2-forward-to-obligation-hyp-equiv

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

Theorem: obligation-hyp-equiv-of-obligation-hyp-fix-1-forward

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

Theorem: obligation-hyp-equiv-of-obligation-hyp-fix-2-forward

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

Theorem: obligation-hyp-kind$inline-of-obligation-hyp-fix-x

(defthm obligation-hyp-kind$inline-of-obligation-hyp-fix-x
  (equal (obligation-hyp-kind$inline (obligation-hyp-fix x))
         (obligation-hyp-kind$inline x)))

Theorem: obligation-hyp-kind$inline-obligation-hyp-equiv-congruence-on-x

(defthm
    obligation-hyp-kind$inline-obligation-hyp-equiv-congruence-on-x
  (implies (obligation-hyp-equiv x x-equiv)
           (equal (obligation-hyp-kind$inline x)
                  (obligation-hyp-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-obligation-hyp-fix

(defthm consp-of-obligation-hyp-fix
  (consp (obligation-hyp-fix x))
  :rule-classes :type-prescription)