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Svtv-line

Svtv-line->lhs

Get the lhs field from a svtv-line.

Signature
(svtv-line->lhs x) → lhs
Arguments: x — Guard (svtv-line-p x).
Returns: lhs — Type (lhs-p lhs).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: svtv-line->lhs$inline

(defun svtv-line->lhs$inline (x)
  (declare (xargs :guard (svtv-line-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'svtv-line->lhs))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (lhs-fix (std::prod-car x)))
         :exec (std::prod-car x))))

Theorem: lhs-p-of-svtv-line->lhs

(defthm lhs-p-of-svtv-line->lhs
  (b* ((lhs (svtv-line->lhs$inline x)))
    (lhs-p lhs))
  :rule-classes :rewrite)

Theorem: svtv-line->lhs$inline-of-svtv-line-fix-x

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

Theorem: svtv-line->lhs$inline-svtv-line-equiv-congruence-on-x

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