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• Expr-value-option-result

Expr-value-option-result-fix

Fixing function for expr-value-option-result structures.

Signature

(expr-value-option-result-fix acl2::x) → new-x

Arguments

acl2::x — Guard (expr-value-option-resultp acl2::x).

Returns

new-x — Type (expr-value-option-resultp new-x).

Definitions and Theorems

Function: expr-value-option-result-fix$inline

(defun expr-value-option-result-fix$inline (acl2::x)
  (declare (xargs :guard (expr-value-option-resultp acl2::x)))
  (mbe :logic
       (case (expr-value-option-result-kind acl2::x)
         (:ok (b* ((get (expr-value-option-fix acl2::x)))
                get))
         (:err (b* ((get (error-fix acl2::x))) get)))
       :exec acl2::x))

Theorem: expr-value-option-resultp-of-expr-value-option-result-fix

(defthm expr-value-option-resultp-of-expr-value-option-result-fix
  (b* ((new-x (expr-value-option-result-fix$inline acl2::x)))
    (expr-value-option-resultp new-x))
  :rule-classes :rewrite)

Theorem: expr-value-option-result-fix-when-expr-value-option-resultp

(defthm expr-value-option-result-fix-when-expr-value-option-resultp
  (implies (expr-value-option-resultp acl2::x)
           (equal (expr-value-option-result-fix acl2::x)
                  acl2::x)))

Function: expr-value-option-result-equiv$inline

(defun expr-value-option-result-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (expr-value-option-resultp acl2::x)
                              (expr-value-option-resultp acl2::y))))
  (equal (expr-value-option-result-fix acl2::x)
         (expr-value-option-result-fix acl2::y)))

Theorem: expr-value-option-result-equiv-is-an-equivalence

(defthm expr-value-option-result-equiv-is-an-equivalence
  (and (booleanp (expr-value-option-result-equiv x y))
       (expr-value-option-result-equiv x x)
       (implies (expr-value-option-result-equiv x y)
                (expr-value-option-result-equiv y x))
       (implies (and (expr-value-option-result-equiv x y)
                     (expr-value-option-result-equiv y z))
                (expr-value-option-result-equiv x z)))
  :rule-classes (:equivalence))

Theorem: expr-value-option-result-equiv-implies-equal-expr-value-option-result-fix-1

(defthm
 expr-value-option-result-equiv-implies-equal-expr-value-option-result-fix-1
 (implies (expr-value-option-result-equiv acl2::x x-equiv)
          (equal (expr-value-option-result-fix acl2::x)
                 (expr-value-option-result-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: expr-value-option-result-fix-under-expr-value-option-result-equiv

(defthm
  expr-value-option-result-fix-under-expr-value-option-result-equiv
  (expr-value-option-result-equiv
       (expr-value-option-result-fix acl2::x)
       acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-expr-value-option-result-fix-1-forward-to-expr-value-option-result-equiv

(defthm
 equal-of-expr-value-option-result-fix-1-forward-to-expr-value-option-result-equiv
 (implies (equal (expr-value-option-result-fix acl2::x)
                 acl2::y)
          (expr-value-option-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-expr-value-option-result-fix-2-forward-to-expr-value-option-result-equiv

(defthm
 equal-of-expr-value-option-result-fix-2-forward-to-expr-value-option-result-equiv
 (implies (equal acl2::x
                 (expr-value-option-result-fix acl2::y))
          (expr-value-option-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: expr-value-option-result-equiv-of-expr-value-option-result-fix-1-forward

(defthm
 expr-value-option-result-equiv-of-expr-value-option-result-fix-1-forward
 (implies (expr-value-option-result-equiv
               (expr-value-option-result-fix acl2::x)
               acl2::y)
          (expr-value-option-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: expr-value-option-result-equiv-of-expr-value-option-result-fix-2-forward

(defthm
 expr-value-option-result-equiv-of-expr-value-option-result-fix-2-forward
 (implies (expr-value-option-result-equiv
               acl2::x
               (expr-value-option-result-fix acl2::y))
          (expr-value-option-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: expr-value-option-result-kind$inline-of-expr-value-option-result-fix-x

(defthm
 expr-value-option-result-kind$inline-of-expr-value-option-result-fix-x
 (equal (expr-value-option-result-kind$inline
             (expr-value-option-result-fix acl2::x))
        (expr-value-option-result-kind$inline acl2::x)))

Theorem: expr-value-option-result-kind$inline-expr-value-option-result-equiv-congruence-on-x

(defthm
 expr-value-option-result-kind$inline-expr-value-option-result-equiv-congruence-on-x
 (implies (expr-value-option-result-equiv acl2::x x-equiv)
          (equal (expr-value-option-result-kind$inline acl2::x)
                 (expr-value-option-result-kind$inline x-equiv)))
 :rule-classes :congruence)

Theorem: expr-value-option-result-fix$inline-of-expr-value-option-result-fix-x

(defthm
 expr-value-option-result-fix$inline-of-expr-value-option-result-fix-x
 (equal (expr-value-option-result-fix$inline
             (expr-value-option-result-fix acl2::x))
        (expr-value-option-result-fix$inline acl2::x)))

Theorem: expr-value-option-result-fix$inline-expr-value-option-result-equiv-congruence-on-x

(defthm
 expr-value-option-result-fix$inline-expr-value-option-result-equiv-congruence-on-x
 (implies (expr-value-option-result-equiv acl2::x x-equiv)
          (equal (expr-value-option-result-fix$inline acl2::x)
                 (expr-value-option-result-fix$inline x-equiv)))
 :rule-classes :congruence)