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Integer-operations

Uint-lt

Less-than comparison of unsigned integer values.

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

Definitions and Theorems

Function: uint-lt

(defun uint-lt (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-lt

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

Theorem: uint-lt-of-uint-fix-left

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

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

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

Theorem: uint-lt-of-uint-fix-right

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

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

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