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Fsuffix

Fsuffix-equiv

Basic equivalence relation for fsuffix structures.

Definitions and Theorems

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)