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Integer-operations

Int-eq

Equality comparison of signed integer values.

Signature
(int-eq left right) → result
Arguments: left — Guard (intp left).; right — Guard (intp right).
Returns: result — Type (boolp result).

Definitions and Theorems

Function: int-eq

(defun int-eq (left right)
  (declare (xargs :guard (and (intp left) (intp right))))
  (declare (xargs :guard (= (int->size left) (int->size right))))
  (b* ((x (int->value left))
       (y (int->value right)))
    (bool (equal x y))))

Theorem: boolp-of-int-eq

(defthm boolp-of-int-eq
  (b* ((result (int-eq left right)))
    (boolp result))
  :rule-classes :rewrite)

Theorem: int-eq-of-int-fix-left

(defthm int-eq-of-int-fix-left
  (equal (int-eq (int-fix left) right)
         (int-eq left right)))

Theorem: int-eq-int-equiv-congruence-on-left

(defthm int-eq-int-equiv-congruence-on-left
  (implies (int-equiv left left-equiv)
           (equal (int-eq left right)
                  (int-eq left-equiv right)))
  :rule-classes :congruence)

Theorem: int-eq-of-int-fix-right

(defthm int-eq-of-int-fix-right
  (equal (int-eq left (int-fix right))
         (int-eq left right)))

Theorem: int-eq-int-equiv-congruence-on-right

(defthm int-eq-int-equiv-congruence-on-right
  (implies (int-equiv right right-equiv)
           (equal (int-eq left right)
                  (int-eq left right-equiv)))
  :rule-classes :congruence)