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Modr/m

Modr/m-fix

Fixing function for modr/m bit structures.

Signature
(modr/m-fix x) → fty::fixed
Arguments: x — Guard (modr/m-p x).
Returns: fty::fixed — Type (modr/m-p fty::fixed).

Definitions and Theorems

Function: modr/m-fix$inline

(defun modr/m-fix$inline (x)
  (declare (xargs :guard (modr/m-p x)))
  (mbe :logic (loghead 8 x) :exec x))

Theorem: modr/m-p-of-modr/m-fix

(defthm modr/m-p-of-modr/m-fix
  (b* ((fty::fixed (modr/m-fix$inline x)))
    (modr/m-p fty::fixed))
  :rule-classes :rewrite)

Theorem: modr/m-fix-when-modr/m-p

(defthm modr/m-fix-when-modr/m-p
  (implies (modr/m-p x)
           (equal (modr/m-fix x) x)))

Function: modr/m-equiv$inline

(defun modr/m-equiv$inline (x y)
  (declare (xargs :guard (and (modr/m-p x) (modr/m-p y))))
  (equal (modr/m-fix x) (modr/m-fix y)))

Theorem: modr/m-equiv-is-an-equivalence

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

Theorem: modr/m-equiv-implies-equal-modr/m-fix-1

(defthm modr/m-equiv-implies-equal-modr/m-fix-1
  (implies (modr/m-equiv x x-equiv)
           (equal (modr/m-fix x)
                  (modr/m-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: modr/m-fix-under-modr/m-equiv

(defthm modr/m-fix-under-modr/m-equiv
  (modr/m-equiv (modr/m-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))