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Expression-tuple-component

Expression-tuple-component->index

Get the index field from a expression-tuple-component.

Signature
(expression-tuple-component->index x) → index
Arguments: x — Guard (expressionp x).
Returns: index — Type (natp index).

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

Definitions and Theorems

Function: expression-tuple-component->index$inline

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

Theorem: natp-of-expression-tuple-component->index

(defthm natp-of-expression-tuple-component->index
  (b* ((index (expression-tuple-component->index$inline x)))
    (natp index))
  :rule-classes :rewrite)

Theorem: expression-tuple-component->index$inline-of-expression-fix-x

(defthm expression-tuple-component->index$inline-of-expression-fix-x
  (equal
       (expression-tuple-component->index$inline (expression-fix x))
       (expression-tuple-component->index$inline x)))

Theorem: expression-tuple-component->index$inline-expression-equiv-congruence-on-x

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

Theorem: expression-tuple-component->index-when-wrong-kind

(defthm expression-tuple-component->index-when-wrong-kind
  (implies (not (equal (expression-kind x)
                       :tuple-component))
           (equal (expression-tuple-component->index x)
                  (nfix nil))))