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Pointed-integers

Schar-write

Representation of a write of a pointed type signed char.

Signature
(schar-write x) → x
Arguments: x — Guard (scharp x).
Returns: x — Type (star (scharp x)).

Definitions and Theorems

Function: schar-write

(defun schar-write (x)
  (declare (xargs :guard (scharp x)))
  (let ((__function__ 'schar-write))
    (declare (ignorable __function__))
    (schar-fix x)))

Theorem: return-type-of-schar-write

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

Theorem: scharp-of-schar-write

(defthm scharp-of-schar-write
  (b* ((x (schar-write x))) (scharp x))
  :rule-classes :rewrite)

Theorem: schar-write-of-schar-fix-x

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

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

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