Get the 2nd field from a abnf::tree-list-tuple3.
(abnf::tree-list-tuple3->2nd abnf::x) → 2nd
This is an ordinary field accessor created by fty::defprod.
Function:
(defun abnf::tree-list-tuple3->2nd$inline (abnf::x) (declare (xargs :guard (abnf::tree-list-tuple3p abnf::x))) (declare (xargs :guard t)) (let ((__function__ 'abnf::tree-list-tuple3->2nd)) (declare (ignorable __function__)) (mbe :logic (b* ((abnf::x (and t abnf::x))) (abnf::tree-list-fix (cdr (std::da-nth 1 abnf::x)))) :exec (cdr (std::da-nth 1 abnf::x)))))
Theorem:
(defthm abnf::tree-listp-of-tree-list-tuple3->2nd (b* ((2nd (abnf::tree-list-tuple3->2nd$inline abnf::x))) (abnf::tree-listp 2nd)) :rule-classes :rewrite)
Theorem:
(defthm abnf::tree-list-tuple3->2nd$inline-of-tree-list-tuple3-fix-x (equal (abnf::tree-list-tuple3->2nd$inline (abnf::tree-list-tuple3-fix abnf::x)) (abnf::tree-list-tuple3->2nd$inline abnf::x)))
Theorem:
(defthm abnf::tree-list-tuple3->2nd$inline-tree-list-tuple3-equiv-congruence-on-x (implies (abnf::tree-list-tuple3-equiv abnf::x abnf::x-equiv) (equal (abnf::tree-list-tuple3->2nd$inline abnf::x) (abnf::tree-list-tuple3->2nd$inline abnf::x-equiv))) :rule-classes :congruence)