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Defbyte-standard-instances

Sbyte64

Fixtype of signed bytes of size 64.

Definitions and Theorems

Function: sbyte64-equiv$inline

(defun sbyte64-equiv$inline (x y)
  (declare (xargs :guard (and (sbyte64p x) (sbyte64p y))))
  (equal (sbyte64-fix x) (sbyte64-fix y)))

Theorem: sbyte64-equiv-is-an-equivalence

(defthm sbyte64-equiv-is-an-equivalence
  (and (booleanp (sbyte64-equiv x y))
       (sbyte64-equiv x x)
       (implies (sbyte64-equiv x y)
                (sbyte64-equiv y x))
       (implies (and (sbyte64-equiv x y)
                     (sbyte64-equiv y z))
                (sbyte64-equiv x z)))
  :rule-classes (:equivalence))

Theorem: sbyte64-equiv-implies-equal-sbyte64-fix-1

(defthm sbyte64-equiv-implies-equal-sbyte64-fix-1
  (implies (sbyte64-equiv x x-equiv)
           (equal (sbyte64-fix x)
                  (sbyte64-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: sbyte64-fix-under-sbyte64-equiv

(defthm sbyte64-fix-under-sbyte64-equiv
  (sbyte64-equiv (sbyte64-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-sbyte64-fix-1-forward-to-sbyte64-equiv

(defthm equal-of-sbyte64-fix-1-forward-to-sbyte64-equiv
  (implies (equal (sbyte64-fix x) y)
           (sbyte64-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-sbyte64-fix-2-forward-to-sbyte64-equiv

(defthm equal-of-sbyte64-fix-2-forward-to-sbyte64-equiv
  (implies (equal x (sbyte64-fix y))
           (sbyte64-equiv x y))
  :rule-classes :forward-chaining)

Theorem: sbyte64-equiv-of-sbyte64-fix-1-forward

(defthm sbyte64-equiv-of-sbyte64-fix-1-forward
  (implies (sbyte64-equiv (sbyte64-fix x) y)
           (sbyte64-equiv x y))
  :rule-classes :forward-chaining)

Theorem: sbyte64-equiv-of-sbyte64-fix-2-forward

(defthm sbyte64-equiv-of-sbyte64-fix-2-forward
  (implies (sbyte64-equiv x (sbyte64-fix y))
           (sbyte64-equiv x y))
  :rule-classes :forward-chaining)

Subtopics

Sbyte64p: Recognizer for sbyte64.
Sbyte64-fix: Fixer for sbyte64.
Sbyte64-ihs-theorems: Theorems about sbyte64 and IHS functions.