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Integer-operations

Uint-gt

Greater-than comparison of unsigned integer values.

Signature
(uint-gt left right) → result
Arguments: left — Guard (uintp left).; right — Guard (uintp right).
Returns: result — Type (boolp result).

Definitions and Theorems

Function: uint-gt

(defun uint-gt (left right)
  (declare (xargs :guard (and (uintp left) (uintp right))))
  (declare (xargs :guard (= (uint->size left)
                            (uint->size right))))
  (b* ((x (uint->value left))
       (y (uint->value right)))
    (bool (> x y))))

Theorem: boolp-of-uint-gt

(defthm boolp-of-uint-gt
  (b* ((result (uint-gt left right)))
    (boolp result))
  :rule-classes :rewrite)

Theorem: uint-gt-of-uint-fix-left

(defthm uint-gt-of-uint-fix-left
  (equal (uint-gt (uint-fix left) right)
         (uint-gt left right)))

Theorem: uint-gt-uint-equiv-congruence-on-left

(defthm uint-gt-uint-equiv-congruence-on-left
  (implies (uint-equiv left left-equiv)
           (equal (uint-gt left right)
                  (uint-gt left-equiv right)))
  :rule-classes :congruence)

Theorem: uint-gt-of-uint-fix-right

(defthm uint-gt-of-uint-fix-right
  (equal (uint-gt left (uint-fix right))
         (uint-gt left right)))

Theorem: uint-gt-uint-equiv-congruence-on-right

(defthm uint-gt-uint-equiv-congruence-on-right
  (implies (uint-equiv right right-equiv)
           (equal (uint-gt left right)
                  (uint-gt left right-equiv)))
  :rule-classes :congruence)