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Cgraph-outedges

Cgraph-outedges->equivs

Get the equivs field from a cgraph-outedges.

Signature
(cgraph-outedges->equivs x) → equivs
Arguments: x — Guard (cgraph-outedges-p x).
Returns: equivs — Type (cgraph-equivlist-p equivs).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: cgraph-outedges->equivs$inline

(defun cgraph-outedges->equivs$inline (x)
  (declare (xargs :guard (cgraph-outedges-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'cgraph-outedges->equivs))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (cgraph-equivlist-fix (cdr (std::da-nth 1 x))))
         :exec (cdr (std::da-nth 1 x)))))

Theorem: cgraph-equivlist-p-of-cgraph-outedges->equivs

(defthm cgraph-equivlist-p-of-cgraph-outedges->equivs
  (b* ((equivs (cgraph-outedges->equivs$inline x)))
    (cgraph-equivlist-p equivs))
  :rule-classes :rewrite)

Theorem: cgraph-outedges->equivs$inline-of-cgraph-outedges-fix-x

(defthm cgraph-outedges->equivs$inline-of-cgraph-outedges-fix-x
  (equal (cgraph-outedges->equivs$inline (cgraph-outedges-fix x))
         (cgraph-outedges->equivs$inline x)))

Theorem: cgraph-outedges->equivs$inline-cgraph-outedges-equiv-congruence-on-x

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