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Rewrite

Rewrite->equiv

Get the equiv field from a rewrite.

Signature
(rewrite->equiv x) → equiv
Arguments: x — Guard (rewrite-p x).
Returns: equiv — Type (pseudo-fnsym-p equiv).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: rewrite->equiv$inline

(defun rewrite->equiv$inline (x)
  (declare (xargs :guard (rewrite-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'rewrite->equiv))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (pseudo-fnsym-fix (std::da-nth 1 x)))
         :exec (std::da-nth 1 x))))

Theorem: pseudo-fnsym-p-of-rewrite->equiv

(defthm pseudo-fnsym-p-of-rewrite->equiv
  (b* ((equiv (rewrite->equiv$inline x)))
    (pseudo-fnsym-p equiv))
  :rule-classes :rewrite)

Theorem: rewrite->equiv$inline-of-rewrite-fix-x

(defthm rewrite->equiv$inline-of-rewrite-fix-x
  (equal (rewrite->equiv$inline (rewrite-fix x))
         (rewrite->equiv$inline x)))

Theorem: rewrite->equiv$inline-rewrite-equiv-congruence-on-x

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