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Aexp-add

Aexp-add->right

Get the right field from a aexp-add.

Signature
(aexp-add->right x) → right
Arguments: x — Guard (aexpp x).
Returns: right — Type (aexpp right).

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

Definitions and Theorems

Function: aexp-add->right$inline

(defun aexp-add->right$inline (x)
  (declare (xargs :guard (aexpp x)))
  (declare (xargs :guard (equal (aexp-kind x) :add)))
  (let ((__function__ 'aexp-add->right))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (aexp-kind x) :add) x)))
           (aexp-fix (std::da-nth 1 (cdr x))))
         :exec (std::da-nth 1 (cdr x)))))

Theorem: aexpp-of-aexp-add->right

(defthm aexpp-of-aexp-add->right
  (b* ((right (aexp-add->right$inline x)))
    (aexpp right))
  :rule-classes :rewrite)

Theorem: aexp-add->right$inline-of-aexp-fix-x

(defthm aexp-add->right$inline-of-aexp-fix-x
  (equal (aexp-add->right$inline (aexp-fix x))
         (aexp-add->right$inline x)))

Theorem: aexp-add->right$inline-aexp-equiv-congruence-on-x

(defthm aexp-add->right$inline-aexp-equiv-congruence-on-x
  (implies (aexp-equiv x x-equiv)
           (equal (aexp-add->right$inline x)
                  (aexp-add->right$inline x-equiv)))
  :rule-classes :congruence)

Theorem: aexp-add->right-when-wrong-kind

(defthm aexp-add->right-when-wrong-kind
  (implies (not (equal (aexp-kind x) :add))
           (equal (aexp-add->right x)
                  (aexp-fix nil))))