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