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Bexpo

Bexpo->prefix

Get the prefix field from a bexpo.

Signature
(bexpo->prefix x) → prefix
Arguments: x — Guard (bexpop x).
Returns: prefix — Type (bexprefixp prefix).

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

Definitions and Theorems

Function: bexpo->prefix$inline

(defun bexpo->prefix$inline (x)
  (declare (xargs :guard (bexpop x)))
  (declare (xargs :guard t))
  (mbe :logic
       (b* ((x (and t x)))
         (bexprefix-fix (car x)))
       :exec (car x)))

Theorem: bexprefixp-of-bexpo->prefix

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

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

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

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

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