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Atc-arrays

Slong-array-integer-write

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

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

Definitions and Theorems

Function: slong-array-integer-write

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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