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Type-array

Type-array->of

Get the of field from a type-array.

Signature
(type-array->of x) → of
Arguments: x — Guard (typep x).
Returns: of — Type (typep of).

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

Definitions and Theorems

Function: type-array->of$inline

(defun type-array->of$inline (x)
  (declare (xargs :guard (typep x)))
  (declare (xargs :guard (equal (type-kind x) :array)))
  (mbe :logic
       (b* ((x (and (equal (type-kind x) :array) x)))
         (type-fix (std::da-nth 0 (cdr x))))
       :exec (std::da-nth 0 (cdr x))))

Theorem: typep-of-type-array->of

(defthm typep-of-type-array->of
  (b* ((of (type-array->of$inline x)))
    (typep of))
  :rule-classes :rewrite)

Theorem: type-array->of$inline-of-type-fix-x

(defthm type-array->of$inline-of-type-fix-x
  (equal (type-array->of$inline (type-fix x))
         (type-array->of$inline x)))

Theorem: type-array->of$inline-type-equiv-congruence-on-x

(defthm type-array->of$inline-type-equiv-congruence-on-x
  (implies (type-equiv x x-equiv)
           (equal (type-array->of$inline x)
                  (type-array->of$inline x-equiv)))
  :rule-classes :congruence)

Theorem: type-array->of-when-wrong-kind

(defthm type-array->of-when-wrong-kind
  (implies (not (equal (type-kind x) :array))
           (equal (type-array->of x)
                  (type-fix nil))))