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Pristate

Pristate->gcc

Get the gcc field from a pristate.

Signature
(pristate->gcc x) → gcc
Arguments: x — Guard (pristatep x).
Returns: gcc — Type (booleanp gcc).

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

Definitions and Theorems

Function: pristate->gcc$inline

(defun pristate->gcc$inline (x)
  (declare (xargs :guard (pristatep x)))
  (declare (xargs :guard t))
  (let ((__function__ 'pristate->gcc))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (bool-fix (cdr (std::da-nth 3 x))))
         :exec (cdr (std::da-nth 3 x)))))

Theorem: booleanp-of-pristate->gcc

(defthm booleanp-of-pristate->gcc
  (b* ((gcc (pristate->gcc$inline x)))
    (booleanp gcc))
  :rule-classes :rewrite)

Theorem: pristate->gcc$inline-of-pristate-fix-x

(defthm pristate->gcc$inline-of-pristate-fix-x
  (equal (pristate->gcc$inline (pristate-fix x))
         (pristate->gcc$inline x)))

Theorem: pristate->gcc$inline-pristate-equiv-congruence-on-x

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