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Atc-arrays

Schar-array-integer-write

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

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

Definitions and Theorems

Function: schar-array-integer-write

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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