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Hex-quad

Hex-quad->3rd

Get the 3rd field from a hex-quad.

Signature
(hex-quad->3rd x) → 3rd
Arguments: x — Guard (hex-quad-p x).
Returns: 3rd — Type (hex-digit-char-p 3rd).

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

Definitions and Theorems

Function: hex-quad->3rd$inline

(defun hex-quad->3rd$inline (x)
  (declare (xargs :guard (hex-quad-p x)))
  (declare (xargs :guard t))
  (mbe :logic
       (b* ((x (and t x)))
         (str::hex-digit-char-fix (car (cdr x))))
       :exec (car (cdr x))))

Theorem: hex-digit-char-p-of-hex-quad->3rd

(defthm hex-digit-char-p-of-hex-quad->3rd
  (b* ((3rd (hex-quad->3rd$inline x)))
    (hex-digit-char-p 3rd))
  :rule-classes :rewrite)

Theorem: hex-quad->3rd$inline-of-hex-quad-fix-x

(defthm hex-quad->3rd$inline-of-hex-quad-fix-x
  (equal (hex-quad->3rd$inline (hex-quad-fix x))
         (hex-quad->3rd$inline x)))

Theorem: hex-quad->3rd$inline-hex-quad-equiv-congruence-on-x

(defthm hex-quad->3rd$inline-hex-quad-equiv-congruence-on-x
  (implies (hex-quad-equiv x x-equiv)
           (equal (hex-quad->3rd$inline x)
                  (hex-quad->3rd$inline x-equiv)))
  :rule-classes :congruence)