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Member-designor-sub

Member-designor-sub->member

Get the member field from a member-designor-sub.

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

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

Definitions and Theorems

Function: member-designor-sub->member$inline

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

Theorem: member-designorp-of-member-designor-sub->member

(defthm member-designorp-of-member-designor-sub->member
  (b* ((member (member-designor-sub->member$inline x)))
    (member-designorp member))
  :rule-classes :rewrite)

Theorem: member-designor-sub->member$inline-of-member-designor-fix-x

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

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

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

Theorem: member-designor-sub->member-when-wrong-kind

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