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Modscope-nested

Modscope-nested->upper

Get the upper field from a modscope-nested.

Signature
(modscope-nested->upper x) → upper
Arguments: x — Guard (modscope-p x).
Returns: upper — Type (modscope-p upper).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: modscope-nested->upper$inline

(defun modscope-nested->upper$inline (x)
  (declare (xargs :guard (modscope-p x)))
  (declare (xargs :guard (equal (modscope-kind x) :nested)))
  (let ((__function__ 'modscope-nested->upper))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (modscope-kind x) :nested)
                      x)))
           (modscope-fix (std::prod-cdr (std::prod-cdr (cdr x)))))
         :exec (std::prod-cdr (std::prod-cdr (cdr x))))))

Theorem: modscope-p-of-modscope-nested->upper

(defthm modscope-p-of-modscope-nested->upper
  (b* ((upper (modscope-nested->upper$inline x)))
    (modscope-p upper))
  :rule-classes :rewrite)

Theorem: modscope-nested->upper$inline-of-modscope-fix-x

(defthm modscope-nested->upper$inline-of-modscope-fix-x
  (equal (modscope-nested->upper$inline (modscope-fix x))
         (modscope-nested->upper$inline x)))

Theorem: modscope-nested->upper$inline-modscope-equiv-congruence-on-x

(defthm modscope-nested->upper$inline-modscope-equiv-congruence-on-x
  (implies (modscope-equiv x x-equiv)
           (equal (modscope-nested->upper$inline x)
                  (modscope-nested->upper$inline x-equiv)))
  :rule-classes :congruence)

Theorem: modscope-nested->upper-when-wrong-kind

(defthm modscope-nested->upper-when-wrong-kind
  (implies (not (equal (modscope-kind x) :nested))
           (equal (modscope-nested->upper x)
                  (modscope-fix nil))))