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Equality-operations

Op-ne

Leo inequality operation.

Signature
(op-ne left right) → result
Arguments: left — Guard (valuep left).; right — Guard (valuep right).
Returns: result — Type (value-resultp result).

Definitions and Theorems

Function: op-ne

(defun op-ne (left right)
  (declare (xargs :guard (and (valuep left) (valuep right))))
  (let ((__function__ 'op-ne))
    (declare (ignorable __function__))
    (if (type-equiv (type-of-value left)
                    (type-of-value right))
        (value-bool (not (value-equiv left right)))
      (reserrf (list :op-ne (value-fix left)
                     (value-fix right))))))

Theorem: value-resultp-of-op-ne

(defthm value-resultp-of-op-ne
  (b* ((result (op-ne left right)))
    (value-resultp result))
  :rule-classes :rewrite)

Theorem: op-ne-of-value-fix-left

(defthm op-ne-of-value-fix-left
  (equal (op-ne (value-fix left) right)
         (op-ne left right)))

Theorem: op-ne-value-equiv-congruence-on-left

(defthm op-ne-value-equiv-congruence-on-left
  (implies (value-equiv left left-equiv)
           (equal (op-ne left right)
                  (op-ne left-equiv right)))
  :rule-classes :congruence)

Theorem: op-ne-of-value-fix-right

(defthm op-ne-of-value-fix-right
  (equal (op-ne left (value-fix right))
         (op-ne left right)))

Theorem: op-ne-value-equiv-congruence-on-right

(defthm op-ne-value-equiv-congruence-on-right
  (implies (value-equiv right right-equiv)
           (equal (op-ne left right)
                  (op-ne left right-equiv)))
  :rule-classes :congruence)