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Ubyte32-option

Ubyte32-option-fix

Fixing function for ubyte32-option structures.

Signature
(ubyte32-option-fix x) → new-x
Arguments: x — Guard (ubyte32-optionp x).
Returns: new-x — Type (ubyte32-optionp new-x).

Definitions and Theorems

Function: ubyte32-option-fix$inline

(defun ubyte32-option-fix$inline (x)
  (declare (xargs :guard (ubyte32-optionp x)))
  (let ((__function__ 'ubyte32-option-fix))
    (declare (ignorable __function__))
    (mbe :logic (cond ((not x) nil)
                      (t (b* ((fty::val (ubyte32-fix x)))
                           fty::val)))
         :exec x)))

Theorem: ubyte32-optionp-of-ubyte32-option-fix

(defthm ubyte32-optionp-of-ubyte32-option-fix
  (b* ((new-x (ubyte32-option-fix$inline x)))
    (ubyte32-optionp new-x))
  :rule-classes :rewrite)

Theorem: ubyte32-option-fix-when-ubyte32-optionp

(defthm ubyte32-option-fix-when-ubyte32-optionp
  (implies (ubyte32-optionp x)
           (equal (ubyte32-option-fix x) x)))

Function: ubyte32-option-equiv$inline

(defun ubyte32-option-equiv$inline (x y)
  (declare (xargs :guard (and (ubyte32-optionp x)
                              (ubyte32-optionp y))))
  (equal (ubyte32-option-fix x)
         (ubyte32-option-fix y)))

Theorem: ubyte32-option-equiv-is-an-equivalence

(defthm ubyte32-option-equiv-is-an-equivalence
  (and (booleanp (ubyte32-option-equiv x y))
       (ubyte32-option-equiv x x)
       (implies (ubyte32-option-equiv x y)
                (ubyte32-option-equiv y x))
       (implies (and (ubyte32-option-equiv x y)
                     (ubyte32-option-equiv y z))
                (ubyte32-option-equiv x z)))
  :rule-classes (:equivalence))

Theorem: ubyte32-option-equiv-implies-equal-ubyte32-option-fix-1

(defthm ubyte32-option-equiv-implies-equal-ubyte32-option-fix-1
  (implies (ubyte32-option-equiv x x-equiv)
           (equal (ubyte32-option-fix x)
                  (ubyte32-option-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: ubyte32-option-fix-under-ubyte32-option-equiv

(defthm ubyte32-option-fix-under-ubyte32-option-equiv
  (ubyte32-option-equiv (ubyte32-option-fix x)
                        x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-ubyte32-option-fix-1-forward-to-ubyte32-option-equiv

(defthm
      equal-of-ubyte32-option-fix-1-forward-to-ubyte32-option-equiv
  (implies (equal (ubyte32-option-fix x) y)
           (ubyte32-option-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-ubyte32-option-fix-2-forward-to-ubyte32-option-equiv

(defthm
      equal-of-ubyte32-option-fix-2-forward-to-ubyte32-option-equiv
  (implies (equal x (ubyte32-option-fix y))
           (ubyte32-option-equiv x y))
  :rule-classes :forward-chaining)

Theorem: ubyte32-option-equiv-of-ubyte32-option-fix-1-forward

(defthm ubyte32-option-equiv-of-ubyte32-option-fix-1-forward
  (implies (ubyte32-option-equiv (ubyte32-option-fix x)
                                 y)
           (ubyte32-option-equiv x y))
  :rule-classes :forward-chaining)

Theorem: ubyte32-option-equiv-of-ubyte32-option-fix-2-forward

(defthm ubyte32-option-equiv-of-ubyte32-option-fix-2-forward
  (implies (ubyte32-option-equiv x (ubyte32-option-fix y))
           (ubyte32-option-equiv x y))
  :rule-classes :forward-chaining)