Get the lsbs-taller field from a sparseint$-concat.
(sparseint$-concat->lsbs-taller x) → lsbs-taller
This is an ordinary field accessor created by fty::defprod.
Function:
(defun sparseint$-concat->lsbs-taller$inline (x) (declare (xargs :guard (sparseint$-p x))) (declare (xargs :guard (equal (sparseint$-kind x) :concat))) (let ((__function__ 'sparseint$-concat->lsbs-taller)) (declare (ignorable __function__)) (mbe :logic (b* ((x (and (equal (sparseint$-kind x) :concat) x))) (acl2::bool-fix (logbitp 0 (car x)))) :exec (logbitp 0 (car x)))))
Theorem:
(defthm booleanp-of-sparseint$-concat->lsbs-taller (b* ((lsbs-taller (sparseint$-concat->lsbs-taller$inline x))) (booleanp lsbs-taller)) :rule-classes :type-prescription)
Theorem:
(defthm sparseint$-concat->lsbs-taller$inline-of-sparseint$-fix-x (equal (sparseint$-concat->lsbs-taller$inline (sparseint$-fix x)) (sparseint$-concat->lsbs-taller$inline x)))
Theorem:
(defthm sparseint$-concat->lsbs-taller$inline-sparseint$-equiv-congruence-on-x (implies (sparseint$-equiv x x-equiv) (equal (sparseint$-concat->lsbs-taller$inline x) (sparseint$-concat->lsbs-taller$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm sparseint$-concat->lsbs-taller-when-wrong-kind (implies (not (equal (sparseint$-kind x) :concat)) (equal (sparseint$-concat->lsbs-taller x) (acl2::bool-fix nil))))