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• Uinteger-format

Uinteger-format-equiv

Basic equivalence relation for uinteger-format structures.

Definitions and Theorems

Function: uinteger-format-equiv$inline

(defun uinteger-format-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (uinteger-formatp acl2::x)
                              (uinteger-formatp acl2::y))))
  (equal (uinteger-format-fix acl2::x)
         (uinteger-format-fix acl2::y)))

Theorem: uinteger-format-equiv-is-an-equivalence

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

Theorem: uinteger-format-equiv-implies-equal-uinteger-format-fix-1

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

Theorem: uinteger-format-fix-under-uinteger-format-equiv

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

Theorem: equal-of-uinteger-format-fix-1-forward-to-uinteger-format-equiv

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

Theorem: equal-of-uinteger-format-fix-2-forward-to-uinteger-format-equiv

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

Theorem: uinteger-format-equiv-of-uinteger-format-fix-1-forward

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

Theorem: uinteger-format-equiv-of-uinteger-format-fix-2-forward

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