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Ringosc3

Ringosc3->n3

Get the n3 field from a ringosc3.

Signature
(ringosc3->n3 x) → n3
Arguments: x — Guard (ringosc3-p x).
Returns: n3 — Type (sig-path-p n3).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: ringosc3->n3$inline

(defun ringosc3->n3$inline (x)
  (declare (xargs :guard (ringosc3-p x)))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'ringosc3->n3))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((x (and t x)))
           (sig-path-fix (cdr (std::da-nth 2 x))))
         :exec (cdr (std::da-nth 2 x)))))

Theorem: sig-path-p-of-ringosc3->n3

(defthm sig-path-p-of-ringosc3->n3
  (b* ((n3 (ringosc3->n3$inline x)))
    (sig-path-p n3))
  :rule-classes :rewrite)

Theorem: ringosc3->n3$inline-of-ringosc3-fix-x

(defthm ringosc3->n3$inline-of-ringosc3-fix-x
  (equal (ringosc3->n3$inline (ringosc3-fix x))
         (ringosc3->n3$inline x)))

Theorem: ringosc3->n3$inline-ringosc3-equiv-congruence-on-x

(defthm ringosc3->n3$inline-ringosc3-equiv-congruence-on-x
  (implies (ringosc3-equiv x x-equiv)
           (equal (ringosc3->n3$inline x)
                  (ringosc3->n3$inline x-equiv)))
  :rule-classes :congruence)