Get the base field from a num-val-direct.
(num-val-direct->base x) → base
This is an ordinary field accessor created by fty::defprod.
Function:
(defun num-val-direct->base$inline (x) (declare (xargs :guard (num-val-p x))) (declare (xargs :guard (equal (num-val-kind x) :direct))) (let ((__function__ 'num-val-direct->base)) (declare (ignorable __function__)) (mbe :logic (b* ((x (and (equal (num-val-kind x) :direct) x))) (num-base-fix (std::da-nth 0 (cdr x)))) :exec (std::da-nth 0 (cdr x)))))
Theorem:
(defthm num-base-p-of-num-val-direct->base (b* ((base (num-val-direct->base$inline x))) (num-base-p base)) :rule-classes :rewrite)
Theorem:
(defthm num-val-direct->base$inline-of-num-val-fix-x (equal (num-val-direct->base$inline (num-val-fix x)) (num-val-direct->base$inline x)))
Theorem:
(defthm num-val-direct->base$inline-num-val-equiv-congruence-on-x (implies (num-val-equiv x x-equiv) (equal (num-val-direct->base$inline x) (num-val-direct->base$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm num-val-direct->base-when-wrong-kind (implies (not (equal (num-val-kind x) :direct)) (equal (num-val-direct->base x) (num-base-fix nil))))