Get the 1st field from a abnf::tree-list-tuple3.
(abnf::tree-list-tuple3->1st abnf::x) → 1st
This is an ordinary field accessor created by fty::defprod.
Function:
(defun abnf::tree-list-tuple3->1st$inline (abnf::x) (declare (xargs :guard (abnf::tree-list-tuple3p abnf::x))) (declare (xargs :guard t)) (let ((__function__ 'abnf::tree-list-tuple3->1st)) (declare (ignorable __function__)) (mbe :logic (b* ((abnf::x (and t abnf::x))) (abnf::tree-list-fix (cdr (std::da-nth 0 abnf::x)))) :exec (cdr (std::da-nth 0 abnf::x)))))
Theorem:
(defthm abnf::tree-listp-of-tree-list-tuple3->1st (b* ((1st (abnf::tree-list-tuple3->1st$inline abnf::x))) (abnf::tree-listp 1st)) :rule-classes :rewrite)
Theorem:
(defthm abnf::tree-list-tuple3->1st$inline-of-tree-list-tuple3-fix-x (equal (abnf::tree-list-tuple3->1st$inline (abnf::tree-list-tuple3-fix abnf::x)) (abnf::tree-list-tuple3->1st$inline abnf::x)))
Theorem:
(defthm abnf::tree-list-tuple3->1st$inline-tree-list-tuple3-equiv-congruence-on-x (implies (abnf::tree-list-tuple3-equiv abnf::x abnf::x-equiv) (equal (abnf::tree-list-tuple3->1st$inline abnf::x) (abnf::tree-list-tuple3->1st$inline abnf::x-equiv))) :rule-classes :congruence)