		Search-engine friendly clone of the ACL2 documentation.

Member-designor-dot

Member-designor-dot->name

Get the name field from a member-designor-dot.

Signature
(member-designor-dot->name x) → name
Arguments: x — Guard (member-designorp x).
Returns: name — Type (identp name).

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

Definitions and Theorems

Function: member-designor-dot->name$inline

(defun member-designor-dot->name$inline (x)
  (declare (xargs :guard (member-designorp x)))
  (declare (xargs :guard (equal (member-designor-kind x) :dot)))
  (mbe :logic
       (b* ((x (and (equal (member-designor-kind x) :dot)
                    x)))
         (ident-fix (cdr (cdr x))))
       :exec (cdr (cdr x))))

Theorem: identp-of-member-designor-dot->name

(defthm identp-of-member-designor-dot->name
  (b* ((name (member-designor-dot->name$inline x)))
    (identp name))
  :rule-classes :rewrite)

Theorem: member-designor-dot->name$inline-of-member-designor-fix-x

(defthm member-designor-dot->name$inline-of-member-designor-fix-x
  (equal (member-designor-dot->name$inline (member-designor-fix x))
         (member-designor-dot->name$inline x)))

Theorem: member-designor-dot->name$inline-member-designor-equiv-congruence-on-x

(defthm
 member-designor-dot->name$inline-member-designor-equiv-congruence-on-x
 (implies (member-designor-equiv x x-equiv)
          (equal (member-designor-dot->name$inline x)
                 (member-designor-dot->name$inline x-equiv)))
 :rule-classes :congruence)

Theorem: member-designor-dot->name-when-wrong-kind

(defthm member-designor-dot->name-when-wrong-kind
  (implies (not (equal (member-designor-kind x) :dot))
           (equal (member-designor-dot->name x)
                  (ident-fix nil))))