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Named-lit-list-map

Named-lit-list-map-equiv

Basic equivalence relation for named-lit-list-map structures.

Definitions and Theorems

Function: named-lit-list-map-equiv$inline

(defun named-lit-list-map-equiv$inline (x acl2::y)
  (declare (xargs :guard (and (named-lit-list-map-p x)
                              (named-lit-list-map-p acl2::y))))
  (equal (named-lit-list-map-fix x)
         (named-lit-list-map-fix acl2::y)))

Theorem: named-lit-list-map-equiv-is-an-equivalence

(defthm named-lit-list-map-equiv-is-an-equivalence
  (and (booleanp (named-lit-list-map-equiv x y))
       (named-lit-list-map-equiv x x)
       (implies (named-lit-list-map-equiv x y)
                (named-lit-list-map-equiv y x))
       (implies (and (named-lit-list-map-equiv x y)
                     (named-lit-list-map-equiv y z))
                (named-lit-list-map-equiv x z)))
  :rule-classes (:equivalence))

Theorem: named-lit-list-map-equiv-implies-equal-named-lit-list-map-fix-1

(defthm
    named-lit-list-map-equiv-implies-equal-named-lit-list-map-fix-1
  (implies (named-lit-list-map-equiv x x-equiv)
           (equal (named-lit-list-map-fix x)
                  (named-lit-list-map-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: named-lit-list-map-fix-under-named-lit-list-map-equiv

(defthm named-lit-list-map-fix-under-named-lit-list-map-equiv
  (named-lit-list-map-equiv (named-lit-list-map-fix x)
                            x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-named-lit-list-map-fix-1-forward-to-named-lit-list-map-equiv

(defthm
 equal-of-named-lit-list-map-fix-1-forward-to-named-lit-list-map-equiv
 (implies (equal (named-lit-list-map-fix x)
                 acl2::y)
          (named-lit-list-map-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-named-lit-list-map-fix-2-forward-to-named-lit-list-map-equiv

(defthm
 equal-of-named-lit-list-map-fix-2-forward-to-named-lit-list-map-equiv
 (implies (equal x (named-lit-list-map-fix acl2::y))
          (named-lit-list-map-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: named-lit-list-map-equiv-of-named-lit-list-map-fix-1-forward

(defthm named-lit-list-map-equiv-of-named-lit-list-map-fix-1-forward
  (implies (named-lit-list-map-equiv (named-lit-list-map-fix x)
                                     acl2::y)
           (named-lit-list-map-equiv x acl2::y))
  :rule-classes :forward-chaining)

Theorem: named-lit-list-map-equiv-of-named-lit-list-map-fix-2-forward

(defthm named-lit-list-map-equiv-of-named-lit-list-map-fix-2-forward
  (implies
       (named-lit-list-map-equiv x (named-lit-list-map-fix acl2::y))
       (named-lit-list-map-equiv x acl2::y))
  :rule-classes :forward-chaining)