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Matchstate

Matchstate->index

Get the index field from a matchstate.

Signature
(matchstate->index x) → index
Arguments: x — Guard (matchstate-p x).
Returns: index — Type (natp index).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: matchstate->index$inline

(defun matchstate->index$inline (x)
  (declare (xargs :guard (matchstate-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'matchstate->index))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (nfix (std::prod-car x)))
         :exec (std::prod-car x))))

Theorem: natp-of-matchstate->index

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

Theorem: matchstate->index$inline-of-matchstate-fix-x

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

Theorem: matchstate->index$inline-matchstate-equiv-congruence-on-x

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