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Alternative

Alternative->product

Get the product field from a alternative.

Signature
(alternative->product x) → product
Arguments: x — Guard (alternativep x).
Returns: product — Type (type-productp product).

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

Definitions and Theorems

Function: alternative->product$inline

(defun alternative->product$inline (x)
  (declare (xargs :guard (alternativep x)))
  (declare (xargs :guard t))
  (let ((__function__ 'alternative->product))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (type-product-fix (cdr (std::da-nth 1 x))))
         :exec (cdr (std::da-nth 1 x)))))

Theorem: type-productp-of-alternative->product

(defthm type-productp-of-alternative->product
  (b* ((product (alternative->product$inline x)))
    (type-productp product))
  :rule-classes :rewrite)

Theorem: alternative->product$inline-of-alternative-fix-x

(defthm alternative->product$inline-of-alternative-fix-x
  (equal (alternative->product$inline (alternative-fix x))
         (alternative->product$inline x)))

Theorem: alternative->product$inline-alternative-equiv-congruence-on-x

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