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Pointed-integers

Sint-write

Representation of a write of a pointed type signed int.

Signature
(sint-write x) → x
Arguments: x — Guard (sintp x).
Returns: x — Type (star (sintp x)).

Definitions and Theorems

Function: sint-write

(defun sint-write (x)
  (declare (xargs :guard (sintp x)))
  (let ((__function__ 'sint-write))
    (declare (ignorable __function__))
    (sint-fix x)))

Theorem: return-type-of-sint-write

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

Theorem: sintp-of-sint-write

(defthm sintp-of-sint-write
  (b* ((x (sint-write x))) (sintp x))
  :rule-classes :rewrite)

Theorem: sint-write-of-sint-fix-x

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

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

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