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Equality-operations

Op-eq

Leo equality operation.

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

Definitions and Theorems

Function: op-eq

(defun op-eq (left right)
  (declare (xargs :guard (and (valuep left) (valuep right))))
  (let ((__function__ 'op-eq))
    (declare (ignorable __function__))
    (if (type-equiv (type-of-value left)
                    (type-of-value right))
        (value-bool (value-equiv left right))
      (reserrf (list :op-eq (value-fix left)
                     (value-fix right))))))

Theorem: value-resultp-of-op-eq

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

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

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

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

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

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

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

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

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