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Hex-pair

Hex-pair->2nd

Get the 2nd field from a hex-pair.

Signature
(hex-pair->2nd x) → 2nd
Arguments: x — Guard (hex-pairp x).
Returns: 2nd — Type (hex-digitp 2nd).

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

Definitions and Theorems

Function: hex-pair->2nd$inline

(defun hex-pair->2nd$inline (x)
  (declare (xargs :guard (hex-pairp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'hex-pair->2nd))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (hex-digit-fix (cdr (std::da-nth 1 (cdr x)))))
         :exec (cdr (std::da-nth 1 (cdr x))))))

Theorem: hex-digitp-of-hex-pair->2nd

(defthm hex-digitp-of-hex-pair->2nd
  (b* ((2nd (hex-pair->2nd$inline x)))
    (hex-digitp 2nd))
  :rule-classes :rewrite)

Theorem: hex-pair->2nd$inline-of-hex-pair-fix-x

(defthm hex-pair->2nd$inline-of-hex-pair-fix-x
  (equal (hex-pair->2nd$inline (hex-pair-fix x))
         (hex-pair->2nd$inline x)))

Theorem: hex-pair->2nd$inline-hex-pair-equiv-congruence-on-x

(defthm hex-pair->2nd$inline-hex-pair-equiv-congruence-on-x
  (implies (hex-pair-equiv x x-equiv)
           (equal (hex-pair->2nd$inline x)
                  (hex-pair->2nd$inline x-equiv)))
  :rule-classes :congruence)