Get the else field from a g-ite.
(g-ite->else x) → else
This is an ordinary field accessor created by defprod.
Function:
(defun g-ite->else$inline (x) (declare (xargs :guard (fgl-object-p x))) (declare (xargs :guard (equal (fgl-object-kind x) :g-ite))) (let ((__function__ 'g-ite->else)) (declare (ignorable __function__)) (mbe :logic (b* ((x (and (equal (fgl-object-kind x) :g-ite) x))) (fgl-object-fix (cdddr x))) :exec (cdddr x))))
Theorem:
(defthm fgl-object-p-of-g-ite->else (b* ((else (g-ite->else$inline x))) (fgl-object-p else)) :rule-classes :rewrite)
Theorem:
(defthm g-ite->else$inline-of-fgl-object-fix-x (equal (g-ite->else$inline (fgl-object-fix x)) (g-ite->else$inline x)))
Theorem:
(defthm g-ite->else$inline-fgl-object-equiv-congruence-on-x (implies (fgl-object-equiv x x-equiv) (equal (g-ite->else$inline x) (g-ite->else$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm g-ite->else-when-wrong-kind (implies (not (equal (fgl-object-kind x) :g-ite)) (equal (g-ite->else x) (fgl-object-fix nil))))