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Dexpo

Dexpo->prefix

Get the prefix field from a dexpo.

Signature
(dexpo->prefix x) → prefix
Arguments: x — Guard (dexpop x).
Returns: prefix — Type (dexprefixp prefix).

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

Definitions and Theorems

Function: dexpo->prefix$inline

(defun dexpo->prefix$inline (x)
  (declare (xargs :guard (dexpop x)))
  (declare (xargs :guard t))
  (mbe :logic
       (b* ((x (and t x)))
         (dexprefix-fix (car x)))
       :exec (car x)))

Theorem: dexprefixp-of-dexpo->prefix

(defthm dexprefixp-of-dexpo->prefix
  (b* ((prefix (dexpo->prefix$inline x)))
    (dexprefixp prefix))
  :rule-classes :rewrite)

Theorem: dexpo->prefix$inline-of-dexpo-fix-x

(defthm dexpo->prefix$inline-of-dexpo-fix-x
  (equal (dexpo->prefix$inline (dexpo-fix x))
         (dexpo->prefix$inline x)))

Theorem: dexpo->prefix$inline-dexpo-equiv-congruence-on-x

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