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