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Cgraph-equivnode

Cgraph-equivnode->equivalence

Get the equivalence field from a cgraph-equivnode.

Signature
(cgraph-equivnode->equivalence x) → equivalence
Arguments: x — Guard (cgraph-equivnode-p x).
Returns: equivalence — Type (fgl-object-p equivalence).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: cgraph-equivnode->equivalence$inline

(defun cgraph-equivnode->equivalence$inline (x)
  (declare (xargs :guard (cgraph-equivnode-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'cgraph-equivnode->equivalence))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (fgl-object-fix (cdr (std::da-nth 0 x))))
         :exec (cdr (std::da-nth 0 x)))))

Theorem: fgl-object-p-of-cgraph-equivnode->equivalence

(defthm fgl-object-p-of-cgraph-equivnode->equivalence
  (b* ((equivalence (cgraph-equivnode->equivalence$inline x)))
    (fgl-object-p equivalence))
  :rule-classes :rewrite)

Theorem: cgraph-equivnode->equivalence$inline-of-cgraph-equivnode-fix-x

(defthm
     cgraph-equivnode->equivalence$inline-of-cgraph-equivnode-fix-x
 (equal
     (cgraph-equivnode->equivalence$inline (cgraph-equivnode-fix x))
     (cgraph-equivnode->equivalence$inline x)))

Theorem: cgraph-equivnode->equivalence$inline-cgraph-equivnode-equiv-congruence-on-x

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