		Search-engine friendly clone of the ACL2 documentation.

Decl-decl

Decl-decl->init

Get the init field from a decl-decl.

Signature
(decl-decl->init x) → init
Arguments: x — Guard (declp x).
Returns: init — Type (initdeclor-listp init).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: decl-decl->init$inline

(defun decl-decl->init$inline (x)
  (declare (xargs :guard (declp x)))
  (declare (xargs :guard (equal (decl-kind x) :decl)))
  (let ((__function__ 'decl-decl->init))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (decl-kind x) :decl) x)))
           (initdeclor-list-fix (std::da-nth 2 (cdr x))))
         :exec (std::da-nth 2 (cdr x)))))

Theorem: initdeclor-listp-of-decl-decl->init

(defthm initdeclor-listp-of-decl-decl->init
  (b* ((init (decl-decl->init$inline x)))
    (initdeclor-listp init))
  :rule-classes :rewrite)

Theorem: decl-decl->init$inline-of-decl-fix-x

(defthm decl-decl->init$inline-of-decl-fix-x
  (equal (decl-decl->init$inline (decl-fix x))
         (decl-decl->init$inline x)))

Theorem: decl-decl->init$inline-decl-equiv-congruence-on-x

(defthm decl-decl->init$inline-decl-equiv-congruence-on-x
  (implies (decl-equiv x x-equiv)
           (equal (decl-decl->init$inline x)
                  (decl-decl->init$inline x-equiv)))
  :rule-classes :congruence)

Theorem: decl-decl->init-when-wrong-kind

(defthm decl-decl->init-when-wrong-kind
  (implies (not (equal (decl-kind x) :decl))
           (equal (decl-decl->init x)
                  (initdeclor-list-fix nil))))