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Hex-string-content

Hex-string-content->first

Get the first field from a hex-string-content.

Signature
(hex-string-content->first x) → first
Arguments: x — Guard (hex-string-contentp x).
Returns: first — Type (hex-pairp first).

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

Definitions and Theorems

Function: hex-string-content->first$inline

(defun hex-string-content->first$inline (x)
  (declare (xargs :guard (hex-string-contentp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'hex-string-content->first))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (hex-pair-fix (cdr (std::da-nth 0 (cdr x)))))
         :exec (cdr (std::da-nth 0 (cdr x))))))

Theorem: hex-pairp-of-hex-string-content->first

(defthm hex-pairp-of-hex-string-content->first
  (b* ((first (hex-string-content->first$inline x)))
    (hex-pairp first))
  :rule-classes :rewrite)

Theorem: hex-string-content->first$inline-of-hex-string-content-fix-x

(defthm hex-string-content->first$inline-of-hex-string-content-fix-x
  (equal
       (hex-string-content->first$inline (hex-string-content-fix x))
       (hex-string-content->first$inline x)))

Theorem: hex-string-content->first$inline-hex-string-content-equiv-congruence-on-x

(defthm
 hex-string-content->first$inline-hex-string-content-equiv-congruence-on-x
 (implies (hex-string-content-equiv x x-equiv)
          (equal (hex-string-content->first$inline x)
                 (hex-string-content->first$inline x-equiv)))
 :rule-classes :congruence)