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Plexeme-ident

Plexeme-ident->ident

Get the ident field from a plexeme-ident.

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

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

Definitions and Theorems

Function: plexeme-ident->ident$inline

(defun plexeme-ident->ident$inline (x)
  (declare (xargs :guard (plexemep x)))
  (declare (xargs :guard (equal (plexeme-kind x) :ident)))
  (mbe :logic
       (b* ((x (and (equal (plexeme-kind x) :ident)
                    x)))
         (ident-fix (std::da-nth 0 (cdr x))))
       :exec (std::da-nth 0 (cdr x))))

Theorem: identp-of-plexeme-ident->ident

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

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

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

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

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

Theorem: plexeme-ident->ident-when-wrong-kind

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