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Hex-string-rest-element

Hex-string-rest-element->pair

Get the pair field from a hex-string-rest-element.

Signature
(hex-string-rest-element->pair x) → pair
Arguments: x — Guard (hex-string-rest-elementp x).
Returns: pair — Type (hex-pairp pair).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: hex-string-rest-element->pair$inline

(defun hex-string-rest-element->pair$inline (x)
  (declare (xargs :guard (hex-string-rest-elementp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'hex-string-rest-element->pair))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (hex-pair-fix (cdr (std::da-nth 1 (cdr x)))))
         :exec (cdr (std::da-nth 1 (cdr x))))))

Theorem: hex-pairp-of-hex-string-rest-element->pair

(defthm hex-pairp-of-hex-string-rest-element->pair
  (b* ((pair (hex-string-rest-element->pair$inline x)))
    (hex-pairp pair))
  :rule-classes :rewrite)

Theorem: hex-string-rest-element->pair$inline-of-hex-string-rest-element-fix-x

(defthm
 hex-string-rest-element->pair$inline-of-hex-string-rest-element-fix-x
 (equal (hex-string-rest-element->pair$inline
             (hex-string-rest-element-fix x))
        (hex-string-rest-element->pair$inline x)))

Theorem: hex-string-rest-element->pair$inline-hex-string-rest-element-equiv-congruence-on-x

(defthm
 hex-string-rest-element->pair$inline-hex-string-rest-element-equiv-congruence-on-x
 (implies (hex-string-rest-element-equiv x x-equiv)
          (equal (hex-string-rest-element->pair$inline x)
                 (hex-string-rest-element->pair$inline x-equiv)))
 :rule-classes :congruence)