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Member-designor-ident

Member-designor-ident->ident

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

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

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

Definitions and Theorems

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

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

Theorem: identp-of-member-designor-ident->ident

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

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

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

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

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

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

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