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• Syntax

Maybe-string-fix

Signature

(maybe-string-fix x) → xx

Arguments

x — Guard (maybe-stringp x).

Returns

xx — Type (maybe-stringp xx).

Definitions and Theorems

Function: maybe-string-fix

(defun maybe-string-fix (x)
  (declare (xargs :guard (maybe-stringp x)))
  (let ((__function__ 'maybe-string-fix))
    (declare (ignorable __function__))
    (mbe :logic (and x (str-fix x))
         :exec x)))

Theorem: maybe-stringp-of-maybe-string-fix

(defthm maybe-stringp-of-maybe-string-fix
  (b* ((xx (maybe-string-fix x)))
    (maybe-stringp xx))
  :rule-classes :rewrite)

Theorem: maybe-string-fix-when-maybe-stringp

(defthm maybe-string-fix-when-maybe-stringp
  (implies (maybe-stringp x)
           (equal (maybe-string-fix x) x)))

Theorem: maybe-string-fix-under-iff

(defthm maybe-string-fix-under-iff
  (iff (maybe-string-fix x) x))

Function: maybe-string-equiv$inline

(defun maybe-string-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (maybe-stringp acl2::x)
                              (maybe-stringp acl2::y))))
  (equal (maybe-string-fix acl2::x)
         (maybe-string-fix acl2::y)))

Theorem: maybe-string-equiv-is-an-equivalence

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

Theorem: maybe-string-equiv-implies-equal-maybe-string-fix-1

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

Theorem: maybe-string-fix-under-maybe-string-equiv

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

Theorem: equal-of-maybe-string-fix-1-forward-to-maybe-string-equiv

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

Theorem: equal-of-maybe-string-fix-2-forward-to-maybe-string-equiv

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

Theorem: maybe-string-equiv-of-maybe-string-fix-1-forward

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

Theorem: maybe-string-equiv-of-maybe-string-fix-2-forward

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

Theorem: maybe-string-equiv-refines-streqv

(defthm maybe-string-equiv-refines-streqv
  (implies (maybe-string-equiv x y)
           (streqv x y))
  :rule-classes (:refinement))