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Sd-key

Sd-key->pat

Get the pat field from a sd-key.

Signature
(sd-key->pat x) → pat
Arguments: x — Guard (sd-key-p x).
Returns: pat — Type (stringp pat).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: sd-key->pat$inline

(defun sd-key->pat$inline (x)
  (declare (xargs :guard (sd-key-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'sd-key->pat))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (str-fix (car (cdr x))))
         :exec (car (cdr x)))))

Theorem: stringp-of-sd-key->pat

(defthm stringp-of-sd-key->pat
  (b* ((pat (sd-key->pat$inline x)))
    (stringp pat))
  :rule-classes :type-prescription)

Theorem: sd-key->pat$inline-of-sd-key-fix-x

(defthm sd-key->pat$inline-of-sd-key-fix-x
  (equal (sd-key->pat$inline (sd-key-fix x))
         (sd-key->pat$inline x)))

Theorem: sd-key->pat$inline-sd-key-equiv-congruence-on-x

(defthm sd-key->pat$inline-sd-key-equiv-congruence-on-x
  (implies (sd-key-equiv x x-equiv)
           (equal (sd-key->pat$inline x)
                  (sd-key->pat$inline x-equiv)))
  :rule-classes :congruence)