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Tree-list-tuple9

Tree-list-tuple9->1st

Get the 1st field from a tree-list-tuple9.

Signature
(tree-list-tuple9->1st x) → 1st
Arguments: x — Guard (tree-list-tuple9p x).
Returns: 1st — Type (tree-listp 1st).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: tree-list-tuple9->1st$inline

(defun tree-list-tuple9->1st$inline (x)
  (declare (xargs :guard (tree-list-tuple9p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'tree-list-tuple9->1st))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (tree-list-fix (cdr (std::da-nth 0 x))))
         :exec (cdr (std::da-nth 0 x)))))

Theorem: tree-listp-of-tree-list-tuple9->1st

(defthm tree-listp-of-tree-list-tuple9->1st
  (b* ((1st (tree-list-tuple9->1st$inline x)))
    (tree-listp 1st))
  :rule-classes :rewrite)

Theorem: tree-list-tuple9->1st$inline-of-tree-list-tuple9-fix-x

(defthm tree-list-tuple9->1st$inline-of-tree-list-tuple9-fix-x
  (equal (tree-list-tuple9->1st$inline (tree-list-tuple9-fix x))
         (tree-list-tuple9->1st$inline x)))

Theorem: tree-list-tuple9->1st$inline-tree-list-tuple9-equiv-congruence-on-x

(defthm
 tree-list-tuple9->1st$inline-tree-list-tuple9-equiv-congruence-on-x
 (implies (tree-list-tuple9-equiv x x-equiv)
          (equal (tree-list-tuple9->1st$inline x)
                 (tree-list-tuple9->1st$inline x-equiv)))
 :rule-classes :congruence)