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Atc-arrays

Sint-array-write

Write an element to an array of type signed int, using a c integer index.

Signature
(sint-array-write array index element) → new-array
Arguments: array — Guard (sint-arrayp array).; index — Guard (cintegerp index).; element — Guard (sintp element).
Returns: new-array — Type (sint-arrayp new-array).

Definitions and Theorems

Function: sint-array-write

(defun sint-array-write (array index element)
  (declare (xargs :guard (and (sint-arrayp array)
                              (cintegerp index)
                              (sintp element))))
  (declare (xargs :guard (sint-array-index-okp array index)))
  (let ((__function__ 'sint-array-write))
    (declare (ignorable __function__))
    (if (mbt (sint-array-index-okp array index))
        (sint-array-of (update-nth (integer-from-cinteger index)
                                   (sint-fix element)
                                   (sint-array->elements array)))
      (sint-array-fix array))))

Theorem: sint-arrayp-of-sint-array-write

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

Theorem: len-of-sint-array->elements-of-sint-array-write

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

Theorem: sint-array-length-of-sint-array-write

(defthm sint-array-length-of-sint-array-write
  (equal (sint-array-length (sint-array-write array index element))
         (sint-array-length array)))

Theorem: sint-array-write-to-integer-write

(defthm sint-array-write-to-integer-write
  (equal
       (sint-array-write array index val)
       (sint-array-integer-write array (integer-from-cinteger index)
                                 val)))

Theorem: sint-array-write-alt-def

(defthm sint-array-write-alt-def
  (implies (and (sint-arrayp array)
                (cintegerp index)
                (sintp elem)
                (sint-array-index-okp array index))
           (equal (sint-array-write array index elem)
                  (value-array-write (integer-from-cinteger index)
                                     elem array))))

Theorem: sint-array-write-of-sint-array-fix-array

(defthm sint-array-write-of-sint-array-fix-array
  (equal (sint-array-write (sint-array-fix array)
                           index element)
         (sint-array-write array index element)))

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

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

Theorem: sint-array-write-of-cinteger-fix-index

(defthm sint-array-write-of-cinteger-fix-index
  (equal (sint-array-write array (cinteger-fix index)
                           element)
         (sint-array-write array index element)))

Theorem: sint-array-write-cinteger-equiv-congruence-on-index

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

Theorem: sint-array-write-of-sint-fix-element

(defthm sint-array-write-of-sint-fix-element
  (equal (sint-array-write array index (sint-fix element))
         (sint-array-write array index element)))

Theorem: sint-array-write-sint-equiv-congruence-on-element

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