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Pointed-integers

Slong-write

Representation of a write of a pointed type signed long.

Signature
(slong-write x) → x
Arguments: x — Guard (slongp x).
Returns: x — Type (star (slongp x)).

Definitions and Theorems

Function: slong-write

(defun slong-write (x)
  (declare (xargs :guard (slongp x)))
  (let ((__function__ 'slong-write))
    (declare (ignorable __function__))
    (slong-fix x)))

Theorem: return-type-of-slong-write

(defthm return-type-of-slong-write
  (b* ((x (slong-write x)))
    (star (slongp x)))
  :rule-classes :rewrite)

Theorem: slongp-of-slong-write

(defthm slongp-of-slong-write
  (b* ((x (slong-write x))) (slongp x))
  :rule-classes :rewrite)

Theorem: slong-write-of-slong-fix-x

(defthm slong-write-of-slong-fix-x
  (equal (slong-write (slong-fix x))
         (slong-write x)))

Theorem: slong-write-slong-equiv-congruence-on-x

(defthm slong-write-slong-equiv-congruence-on-x
  (implies (slong-equiv x x-equiv)
           (equal (slong-write x)
                  (slong-write x-equiv)))
  :rule-classes :congruence)