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Name-indexed

Name-indexed->index

Get the index field from a name-indexed.

Signature
(name-indexed->index x) → index
Arguments: x — Guard (namep x).
Returns: index — Type (natp index).

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

Definitions and Theorems

Function: name-indexed->index$inline

(defun name-indexed->index$inline (x)
  (declare (xargs :guard (namep x)))
  (declare (xargs :guard (equal (name-kind x) :indexed)))
  (let ((__function__ 'name-indexed->index))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (name-kind x) :indexed) x)))
           (nfix (std::da-nth 1 (cdr x))))
         :exec (std::da-nth 1 (cdr x)))))

Theorem: natp-of-name-indexed->index

(defthm natp-of-name-indexed->index
  (b* ((index (name-indexed->index$inline x)))
    (natp index))
  :rule-classes :rewrite)

Theorem: name-indexed->index$inline-of-name-fix-x

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

Theorem: name-indexed->index$inline-name-equiv-congruence-on-x

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

Theorem: name-indexed->index-when-wrong-kind

(defthm name-indexed->index-when-wrong-kind
  (implies (not (equal (name-kind x) :indexed))
           (equal (name-indexed->index x)
                  (nfix nil))))