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Defbyte-standard-instances

Sbyte32

Fixtype of signed bytes of size 32.

Definitions and Theorems

Function: sbyte32-equiv$inline

(defun sbyte32-equiv$inline (x y)
  (declare (xargs :guard (and (sbyte32p x) (sbyte32p y))))
  (equal (sbyte32-fix x) (sbyte32-fix y)))

Theorem: sbyte32-equiv-is-an-equivalence

(defthm sbyte32-equiv-is-an-equivalence
  (and (booleanp (sbyte32-equiv x y))
       (sbyte32-equiv x x)
       (implies (sbyte32-equiv x y)
                (sbyte32-equiv y x))
       (implies (and (sbyte32-equiv x y)
                     (sbyte32-equiv y z))
                (sbyte32-equiv x z)))
  :rule-classes (:equivalence))

Theorem: sbyte32-equiv-implies-equal-sbyte32-fix-1

(defthm sbyte32-equiv-implies-equal-sbyte32-fix-1
  (implies (sbyte32-equiv x x-equiv)
           (equal (sbyte32-fix x)
                  (sbyte32-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: sbyte32-fix-under-sbyte32-equiv

(defthm sbyte32-fix-under-sbyte32-equiv
  (sbyte32-equiv (sbyte32-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-sbyte32-fix-1-forward-to-sbyte32-equiv

(defthm equal-of-sbyte32-fix-1-forward-to-sbyte32-equiv
  (implies (equal (sbyte32-fix x) y)
           (sbyte32-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-sbyte32-fix-2-forward-to-sbyte32-equiv

(defthm equal-of-sbyte32-fix-2-forward-to-sbyte32-equiv
  (implies (equal x (sbyte32-fix y))
           (sbyte32-equiv x y))
  :rule-classes :forward-chaining)

Theorem: sbyte32-equiv-of-sbyte32-fix-1-forward

(defthm sbyte32-equiv-of-sbyte32-fix-1-forward
  (implies (sbyte32-equiv (sbyte32-fix x) y)
           (sbyte32-equiv x y))
  :rule-classes :forward-chaining)

Theorem: sbyte32-equiv-of-sbyte32-fix-2-forward

(defthm sbyte32-equiv-of-sbyte32-fix-2-forward
  (implies (sbyte32-equiv x (sbyte32-fix y))
           (sbyte32-equiv x y))
  :rule-classes :forward-chaining)

Subtopics

Sbyte32p: Recognizer for sbyte32.
Sbyte32-fix: Fixer for sbyte32.
Sbyte32-ihs-theorems: Theorems about sbyte32 and IHS functions.