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• Import

Import-equiv

Basic equivalence relation for import structures.

Definitions and Theorems

Function: import-equiv$inline

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

Theorem: import-equiv-is-an-equivalence

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

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

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

Theorem: import-fix-under-import-equiv

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

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

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

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

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

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

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

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

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