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• Jparam

Jparam-equiv

Basic equivalence relation for jparam structures.

Definitions and Theorems

Function: jparam-equiv$inline

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

Theorem: jparam-equiv-is-an-equivalence

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

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

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

Theorem: jparam-fix-under-jparam-equiv

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

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

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

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

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

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

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

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

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