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• Fgl-function-mode

Fgl-function-mode-fix

Fixing function for fgl-function-mode bit structures.

Signature

(fgl-function-mode-fix x) → fty::fixed

Arguments

x — Guard (fgl-function-mode-p x).

Returns

fty::fixed — Type (fgl-function-mode-p fty::fixed).

Definitions and Theorems

Function: fgl-function-mode-fix

(defun fgl-function-mode-fix (x)
  (declare (xargs :guard (fgl-function-mode-p x)))
  (let ((__function__ 'fgl-function-mode-fix))
    (declare (ignorable __function__))
    (mbe :logic (loghead 6 x) :exec x)))

Theorem: fgl-function-mode-p-of-fgl-function-mode-fix

(defthm fgl-function-mode-p-of-fgl-function-mode-fix
  (b* ((fty::fixed (fgl-function-mode-fix x)))
    (fgl-function-mode-p fty::fixed))
  :rule-classes :rewrite)

Theorem: fgl-function-mode-fix-when-fgl-function-mode-p

(defthm fgl-function-mode-fix-when-fgl-function-mode-p
  (implies (fgl-function-mode-p x)
           (equal (fgl-function-mode-fix x) x)))

Function: fgl-function-mode-equiv$inline

(defun fgl-function-mode-equiv$inline (x y)
  (declare (xargs :guard (and (fgl-function-mode-p x)
                              (fgl-function-mode-p y))))
  (equal (fgl-function-mode-fix x)
         (fgl-function-mode-fix y)))

Theorem: fgl-function-mode-equiv-is-an-equivalence

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

Theorem: fgl-function-mode-equiv-implies-equal-fgl-function-mode-fix-1

(defthm
      fgl-function-mode-equiv-implies-equal-fgl-function-mode-fix-1
  (implies (fgl-function-mode-equiv x x-equiv)
           (equal (fgl-function-mode-fix x)
                  (fgl-function-mode-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: fgl-function-mode-fix-under-fgl-function-mode-equiv

(defthm fgl-function-mode-fix-under-fgl-function-mode-equiv
  (fgl-function-mode-equiv (fgl-function-mode-fix x)
                           x)
  :rule-classes (:rewrite :rewrite-quoted-constant))