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• Sd-key

Sd-key->index

Get the index field from a sd-key.

Signature

(sd-key->index x) → index

Arguments

x — Guard (sd-key-p x).

Returns

index — Type (maybe-natp index).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: sd-key->index$inline

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

Theorem: maybe-natp-of-sd-key->index

(defthm maybe-natp-of-sd-key->index
  (b* ((index (sd-key->index$inline x)))
    (maybe-natp index))
  :rule-classes :type-prescription)

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

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

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

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