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• Aignet-output-range-map

Aignet-output-range-map-equiv

Basic equivalence relation for aignet-output-range-map structures.

Definitions and Theorems

Function: aignet-output-range-map-equiv$inline

(defun aignet-output-range-map-equiv$inline (x acl2::y)
  (declare (xargs :guard (and (aignet-output-range-map-p x)
                              (aignet-output-range-map-p acl2::y))))
  (equal (aignet-output-range-map-fix x)
         (aignet-output-range-map-fix acl2::y)))

Theorem: aignet-output-range-map-equiv-is-an-equivalence

(defthm aignet-output-range-map-equiv-is-an-equivalence
  (and (booleanp (aignet-output-range-map-equiv x y))
       (aignet-output-range-map-equiv x x)
       (implies (aignet-output-range-map-equiv x y)
                (aignet-output-range-map-equiv y x))
       (implies (and (aignet-output-range-map-equiv x y)
                     (aignet-output-range-map-equiv y z))
                (aignet-output-range-map-equiv x z)))
  :rule-classes (:equivalence))

Theorem: aignet-output-range-map-equiv-implies-equal-aignet-output-range-map-fix-1

(defthm
 aignet-output-range-map-equiv-implies-equal-aignet-output-range-map-fix-1
 (implies (aignet-output-range-map-equiv x x-equiv)
          (equal (aignet-output-range-map-fix x)
                 (aignet-output-range-map-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: aignet-output-range-map-fix-under-aignet-output-range-map-equiv

(defthm
    aignet-output-range-map-fix-under-aignet-output-range-map-equiv
  (aignet-output-range-map-equiv (aignet-output-range-map-fix x)
                                 x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-aignet-output-range-map-fix-1-forward-to-aignet-output-range-map-equiv

(defthm
 equal-of-aignet-output-range-map-fix-1-forward-to-aignet-output-range-map-equiv
 (implies (equal (aignet-output-range-map-fix x)
                 acl2::y)
          (aignet-output-range-map-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-aignet-output-range-map-fix-2-forward-to-aignet-output-range-map-equiv

(defthm
 equal-of-aignet-output-range-map-fix-2-forward-to-aignet-output-range-map-equiv
 (implies (equal x (aignet-output-range-map-fix acl2::y))
          (aignet-output-range-map-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: aignet-output-range-map-equiv-of-aignet-output-range-map-fix-1-forward

(defthm
 aignet-output-range-map-equiv-of-aignet-output-range-map-fix-1-forward
 (implies
      (aignet-output-range-map-equiv (aignet-output-range-map-fix x)
                                     acl2::y)
      (aignet-output-range-map-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: aignet-output-range-map-equiv-of-aignet-output-range-map-fix-2-forward

(defthm
 aignet-output-range-map-equiv-of-aignet-output-range-map-fix-2-forward
 (implies (aignet-output-range-map-equiv
               x (aignet-output-range-map-fix acl2::y))
          (aignet-output-range-map-equiv x acl2::y))
 :rule-classes :forward-chaining)