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Qualified-ident

Qualified-ident->ident

Get the ident field from a qualified-ident.

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

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

Definitions and Theorems

Function: qualified-ident->ident$inline

(defun qualified-ident->ident$inline (x)
  (declare (xargs :guard (qualified-identp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'qualified-ident->ident))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (ident-fix (cdr (std::da-nth 1 x))))
         :exec (cdr (std::da-nth 1 x)))))

Theorem: identp-of-qualified-ident->ident

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

Theorem: qualified-ident->ident$inline-of-qualified-ident-fix-x

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

Theorem: qualified-ident->ident$inline-qualified-ident-equiv-congruence-on-x

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