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• Atc-arrays

Ullong-array-read

Read an element from an array of type unsigned long long, using a C integer index.

Signature

(ullong-array-read array index) → element

Arguments

array — Guard (ullong-arrayp array).

index — Guard (cintegerp index).

Returns

element — Type (ullongp element).

Definitions and Theorems

Function: ullong-array-read

(defun ullong-array-read (array index)
  (declare (xargs :guard (and (ullong-arrayp array)
                              (cintegerp index))))
  (declare (xargs :guard (ullong-array-index-okp array index)))
  (let ((__function__ 'ullong-array-read))
    (declare (ignorable __function__))
    (ullong-fix (nth (integer-from-cinteger index)
                     (ullong-array->elements array)))))

Theorem: ullongp-of-ullong-array-read

(defthm ullongp-of-ullong-array-read
  (b* ((element (ullong-array-read array index)))
    (ullongp element))
  :rule-classes :rewrite)

Theorem: ullong-array-read-alt-def

(defthm ullong-array-read-alt-def
  (implies (and (ullong-arrayp array)
                (cintegerp index)
                (ullong-array-index-okp array index))
           (equal (ullong-array-read array index)
                  (value-array-read (integer-from-cinteger index)
                                    array))))

Theorem: ullong-array-read-of-ullong-array-fix-array

(defthm ullong-array-read-of-ullong-array-fix-array
  (equal (ullong-array-read (ullong-array-fix array)
                            index)
         (ullong-array-read array index)))

Theorem: ullong-array-read-ullong-array-equiv-congruence-on-array

(defthm ullong-array-read-ullong-array-equiv-congruence-on-array
  (implies (ullong-array-equiv array array-equiv)
           (equal (ullong-array-read array index)
                  (ullong-array-read array-equiv index)))
  :rule-classes :congruence)

Theorem: ullong-array-read-of-cinteger-fix-index

(defthm ullong-array-read-of-cinteger-fix-index
  (equal (ullong-array-read array (cinteger-fix index))
         (ullong-array-read array index)))

Theorem: ullong-array-read-cinteger-equiv-congruence-on-index

(defthm ullong-array-read-cinteger-equiv-congruence-on-index
  (implies (cinteger-equiv index index-equiv)
           (equal (ullong-array-read array index)
                  (ullong-array-read array index-equiv)))
  :rule-classes :congruence)