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Atc-arrays

Sshort-array-integer-write

Write an element to an array of type signed short, using an ACL2 integer index.

Signature
(sshort-array-integer-write array index element) → new-array
Arguments: array — Guard (sshort-arrayp array).; index — Guard (integerp index).; element — Guard (sshortp element).
Returns: new-array — Type (sshort-arrayp new-array).

Definitions and Theorems

Function: sshort-array-integer-write

(defun sshort-array-integer-write (array index element)
  (declare (xargs :guard (and (sshort-arrayp array)
                              (integerp index)
                              (sshortp element))))
  (declare
       (xargs :guard (sshort-array-integer-index-okp array index)))
  (let ((__function__ 'sshort-array-integer-write))
    (declare (ignorable __function__))
    (b* ((array (sshort-array-fix array))
         (index (ifix index))
         (element (sshort-fix element)))
      (if (mbt (sshort-array-integer-index-okp array index))
          (sshort-array-of
               (update-nth index
                           element (sshort-array->elements array)))
        array))))

Theorem: sshort-arrayp-of-sshort-array-integer-write

(defthm sshort-arrayp-of-sshort-array-integer-write
  (b* ((new-array (sshort-array-integer-write array index element)))
    (sshort-arrayp new-array))
  :rule-classes :rewrite)

Theorem: len-of-sshort-array->elements-of-sshort-array-integer-write

(defthm len-of-sshort-array->elements-of-sshort-array-integer-write
 (equal (len (sshort-array->elements
                  (sshort-array-integer-write array index element)))
        (len (sshort-array->elements array))))

Theorem: sshort-array-length-of-sshort-array-integer-write

(defthm sshort-array-length-of-sshort-array-integer-write
  (equal (sshort-array-length
              (sshort-array-integer-write array index element))
         (sshort-array-length array)))

Theorem: sshort-array-integer-write-alt-def

(defthm sshort-array-integer-write-alt-def
  (implies (and (sshort-arrayp array)
                (integerp index)
                (sshortp elem)
                (sshort-array-integer-index-okp array index))
           (equal (sshort-array-integer-write array index elem)
                  (value-array-write index elem array))))

Theorem: sshort-array-integer-write-of-sshort-array-fix-array

(defthm sshort-array-integer-write-of-sshort-array-fix-array
  (equal (sshort-array-integer-write (sshort-array-fix array)
                                     index element)
         (sshort-array-integer-write array index element)))

Theorem: sshort-array-integer-write-sshort-array-equiv-congruence-on-array

(defthm
  sshort-array-integer-write-sshort-array-equiv-congruence-on-array
 (implies
     (sshort-array-equiv array array-equiv)
     (equal (sshort-array-integer-write array index element)
            (sshort-array-integer-write array-equiv index element)))
 :rule-classes :congruence)

Theorem: sshort-array-integer-write-of-ifix-index

(defthm sshort-array-integer-write-of-ifix-index
  (equal (sshort-array-integer-write array (ifix index)
                                     element)
         (sshort-array-integer-write array index element)))

Theorem: sshort-array-integer-write-int-equiv-congruence-on-index

(defthm sshort-array-integer-write-int-equiv-congruence-on-index
 (implies
     (acl2::int-equiv index index-equiv)
     (equal (sshort-array-integer-write array index element)
            (sshort-array-integer-write array index-equiv element)))
 :rule-classes :congruence)

Theorem: sshort-array-integer-write-of-sshort-fix-element

(defthm sshort-array-integer-write-of-sshort-fix-element
  (equal
       (sshort-array-integer-write array index (sshort-fix element))
       (sshort-array-integer-write array index element)))

Theorem: sshort-array-integer-write-sshort-equiv-congruence-on-element

(defthm
      sshort-array-integer-write-sshort-equiv-congruence-on-element
 (implies
     (sshort-equiv element element-equiv)
     (equal (sshort-array-integer-write array index element)
            (sshort-array-integer-write array index element-equiv)))
 :rule-classes :congruence)