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Pointed-integers

Sllong-write

Representation of a write of a pointed type signed long long.

Signature
(sllong-write x) → x
Arguments: x — Guard (sllongp x).
Returns: x — Type (star (sllongp x)).

Definitions and Theorems

Function: sllong-write

(defun sllong-write (x)
  (declare (xargs :guard (sllongp x)))
  (let ((__function__ 'sllong-write))
    (declare (ignorable __function__))
    (sllong-fix x)))

Theorem: return-type-of-sllong-write

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

Theorem: sllongp-of-sllong-write

(defthm sllongp-of-sllong-write
  (b* ((x (sllong-write x))) (sllongp x))
  :rule-classes :rewrite)

Theorem: sllong-write-of-sllong-fix-x

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

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

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