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Type-set

Type-set->element

Get the element field from a type-set.

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

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

Definitions and Theorems

Function: type-set->element$inline

(defun type-set->element$inline (x)
  (declare (xargs :guard (typep x)))
  (declare (xargs :guard (equal (type-kind x) :set)))
  (let ((__function__ 'type-set->element))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (type-kind x) :set) x)))
           (type-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: typep-of-type-set->element

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

Theorem: type-set->element$inline-of-type-fix-x

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

Theorem: type-set->element$inline-type-equiv-congruence-on-x

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

Theorem: type-set->element-when-wrong-kind

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