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• Symbol-value-option

Symbol-value-option-fix

Fixing function for symbol-value-option structures.

Signature

(symbol-value-option-fix x) → new-x

Arguments

x — Guard (symbol-value-optionp x).

Returns

new-x — Type (symbol-value-optionp new-x).

Definitions and Theorems

Function: symbol-value-option-fix$inline

(defun symbol-value-option-fix$inline (x)
  (declare (xargs :guard (symbol-value-optionp x)))
  (let ((__function__ 'symbol-value-option-fix))
    (declare (ignorable __function__))
    (mbe :logic (cond ((not x) nil)
                      (t (b* ((fty::val (symbol-value-fix x)))
                           fty::val)))
         :exec x)))

Theorem: symbol-value-optionp-of-symbol-value-option-fix

(defthm symbol-value-optionp-of-symbol-value-option-fix
  (b* ((new-x (symbol-value-option-fix$inline x)))
    (symbol-value-optionp new-x))
  :rule-classes :rewrite)

Theorem: symbol-value-option-fix-when-symbol-value-optionp

(defthm symbol-value-option-fix-when-symbol-value-optionp
  (implies (symbol-value-optionp x)
           (equal (symbol-value-option-fix x) x)))

Function: symbol-value-option-equiv$inline

(defun symbol-value-option-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (symbol-value-optionp acl2::x)
                              (symbol-value-optionp acl2::y))))
  (equal (symbol-value-option-fix acl2::x)
         (symbol-value-option-fix acl2::y)))

Theorem: symbol-value-option-equiv-is-an-equivalence

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

Theorem: symbol-value-option-equiv-implies-equal-symbol-value-option-fix-1

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

Theorem: symbol-value-option-fix-under-symbol-value-option-equiv

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

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

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

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

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

Theorem: symbol-value-option-equiv-of-symbol-value-option-fix-1-forward

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

Theorem: symbol-value-option-equiv-of-symbol-value-option-fix-2-forward

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