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• Char-val

Char-val-equiv

Basic equivalence relation for char-val structures.

Definitions and Theorems

Function: char-val-equiv$inline

(defun char-val-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (char-val-p acl2::x)
                              (char-val-p acl2::y))))
  (equal (char-val-fix acl2::x)
         (char-val-fix acl2::y)))

Theorem: char-val-equiv-is-an-equivalence

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

Theorem: char-val-equiv-implies-equal-char-val-fix-1

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

Theorem: char-val-fix-under-char-val-equiv

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

Theorem: equal-of-char-val-fix-1-forward-to-char-val-equiv

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

Theorem: equal-of-char-val-fix-2-forward-to-char-val-equiv

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

Theorem: char-val-equiv-of-char-val-fix-1-forward

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

Theorem: char-val-equiv-of-char-val-fix-2-forward

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