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Fsuffix

Fsuffix-fix

Fixing function for fsuffix structures.

Signature
(fsuffix-fix x) → new-x
Arguments: x — Guard (fsuffixp x).
Returns: new-x — Type (fsuffixp new-x).

Definitions and Theorems

Function: fsuffix-fix$inline

(defun fsuffix-fix$inline (x)
  (declare (xargs :guard (fsuffixp x)))
  (let ((__function__ 'fsuffix-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (fsuffix-kind x)
           (:locase-f (cons :locase-f (list)))
           (:upcase-f (cons :upcase-f (list)))
           (:locase-l (cons :locase-l (list)))
           (:upcase-l (cons :upcase-l (list))))
         :exec x)))

Theorem: fsuffixp-of-fsuffix-fix

(defthm fsuffixp-of-fsuffix-fix
  (b* ((new-x (fsuffix-fix$inline x)))
    (fsuffixp new-x))
  :rule-classes :rewrite)

Theorem: fsuffix-fix-when-fsuffixp

(defthm fsuffix-fix-when-fsuffixp
  (implies (fsuffixp x)
           (equal (fsuffix-fix x) x)))

Function: fsuffix-equiv$inline

(defun fsuffix-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (fsuffixp acl2::x)
                              (fsuffixp acl2::y))))
  (equal (fsuffix-fix acl2::x)
         (fsuffix-fix acl2::y)))

Theorem: fsuffix-equiv-is-an-equivalence

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

Theorem: fsuffix-equiv-implies-equal-fsuffix-fix-1

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

Theorem: fsuffix-fix-under-fsuffix-equiv

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

Theorem: equal-of-fsuffix-fix-1-forward-to-fsuffix-equiv

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

Theorem: equal-of-fsuffix-fix-2-forward-to-fsuffix-equiv

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

Theorem: fsuffix-equiv-of-fsuffix-fix-1-forward

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

Theorem: fsuffix-equiv-of-fsuffix-fix-2-forward

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

Theorem: fsuffix-kind$inline-of-fsuffix-fix-x

(defthm fsuffix-kind$inline-of-fsuffix-fix-x
  (equal (fsuffix-kind$inline (fsuffix-fix x))
         (fsuffix-kind$inline x)))

Theorem: fsuffix-kind$inline-fsuffix-equiv-congruence-on-x

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

Theorem: consp-of-fsuffix-fix

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