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• Gout

Gout->thm-index

Get the thm-index field from a gout.

Signature

(gout->thm-index x) → thm-index

Arguments

x — Guard (goutp x).

Returns

thm-index — Type (posp thm-index).

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

Definitions and Theorems

Function: gout->thm-index$inline

(defun gout->thm-index$inline (x)
  (declare (xargs :guard (goutp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'gout->thm-index))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (pos-fix (cdr (std::da-nth 1 x))))
         :exec (cdr (std::da-nth 1 x)))))

Theorem: posp-of-gout->thm-index

(defthm posp-of-gout->thm-index
  (b* ((thm-index (gout->thm-index$inline x)))
    (posp thm-index))
  :rule-classes :rewrite)

Theorem: gout->thm-index$inline-of-gout-fix-x

(defthm gout->thm-index$inline-of-gout-fix-x
  (equal (gout->thm-index$inline (gout-fix x))
         (gout->thm-index$inline x)))

Theorem: gout->thm-index$inline-gout-equiv-congruence-on-x

(defthm gout->thm-index$inline-gout-equiv-congruence-on-x
  (implies (gout-equiv x x-equiv)
           (equal (gout->thm-index$inline x)
                  (gout->thm-index$inline x-equiv)))
  :rule-classes :congruence)