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Feat

Feat->base

Get the base field from a feat.

Signature
(feat->base x) → base
Arguments: x — Guard (featp x).
Returns: base — Type (feat-basep base).

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

Definitions and Theorems

Function: feat->base$inline

(defun feat->base$inline (x)
  (declare (xargs :guard (featp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'feat->base))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (feat-base-fix (cdr (std::da-nth 0 x))))
         :exec (cdr (std::da-nth 0 x)))))

Theorem: feat-basep-of-feat->base

(defthm feat-basep-of-feat->base
  (b* ((base (feat->base$inline x)))
    (feat-basep base))
  :rule-classes :rewrite)

Theorem: feat->base$inline-of-feat-fix-x

(defthm feat->base$inline-of-feat-fix-x
  (equal (feat->base$inline (feat-fix x))
         (feat->base$inline x)))

Theorem: feat->base$inline-feat-equiv-congruence-on-x

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