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Ringosc3

Ringosc3->inv2

Get the inv2 field from a ringosc3.

Signature
(ringosc3->inv2 x) → inv2
Arguments: x — Guard (ringosc3-p x).
Returns: inv2 — Type (inverter-p inv2).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: ringosc3->inv2$inline

(defun ringosc3->inv2$inline (x)
  (declare (xargs :guard (ringosc3-p x)))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'ringosc3->inv2))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((x (and t x)))
           (inverter-fix (cdr (std::da-nth 4 x))))
         :exec (cdr (std::da-nth 4 x)))))

Theorem: inverter-p-of-ringosc3->inv2

(defthm inverter-p-of-ringosc3->inv2
  (b* ((inv2 (ringosc3->inv2$inline x)))
    (inverter-p inv2))
  :rule-classes :rewrite)

Theorem: ringosc3->inv2$inline-of-ringosc3-fix-x

(defthm ringosc3->inv2$inline-of-ringosc3-fix-x
  (equal (ringosc3->inv2$inline (ringosc3-fix x))
         (ringosc3->inv2$inline x)))

Theorem: ringosc3->inv2$inline-ringosc3-equiv-congruence-on-x

(defthm ringosc3->inv2$inline-ringosc3-equiv-congruence-on-x
  (implies (ringosc3-equiv x x-equiv)
           (equal (ringosc3->inv2$inline x)
                  (ringosc3->inv2$inline x-equiv)))
  :rule-classes :congruence)