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Rewrite

Rewrite->lhs

Get the lhs field from a rewrite.

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

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: rewrite->lhs$inline

(defun rewrite->lhs$inline (x)
  (declare (xargs :guard (rewrite-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'rewrite->lhs))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (pseudo-term-fix (std::da-nth 2 x)))
         :exec (std::da-nth 2 x))))

Theorem: pseudo-termp-of-rewrite->lhs

(defthm pseudo-termp-of-rewrite->lhs
  (b* ((lhs (rewrite->lhs$inline x)))
    (pseudo-termp lhs))
  :rule-classes :rewrite)

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

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

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

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