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Valid-scope

Valid-scope->ord

Get the ord field from a valid-scope.

Signature
(valid-scope->ord x) → ord
Arguments: x — Guard (valid-scopep x).
Returns: ord — Type (valid-ord-scopep ord).

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

Definitions and Theorems

Function: valid-scope->ord$inline

(defun valid-scope->ord$inline (x)
  (declare (xargs :guard (valid-scopep x)))
  (declare (xargs :guard t))
  (mbe :logic
       (b* ((x (and t x)))
         (valid-ord-scope-fix (cdr (std::da-nth 0 x))))
       :exec (cdr (std::da-nth 0 x))))

Theorem: valid-ord-scopep-of-valid-scope->ord

(defthm valid-ord-scopep-of-valid-scope->ord
  (b* ((ord (valid-scope->ord$inline x)))
    (valid-ord-scopep ord))
  :rule-classes :rewrite)

Theorem: valid-scope->ord$inline-of-valid-scope-fix-x

(defthm valid-scope->ord$inline-of-valid-scope-fix-x
  (equal (valid-scope->ord$inline (valid-scope-fix x))
         (valid-scope->ord$inline x)))

Theorem: valid-scope->ord$inline-valid-scope-equiv-congruence-on-x

(defthm valid-scope->ord$inline-valid-scope-equiv-congruence-on-x
  (implies (valid-scope-equiv x x-equiv)
           (equal (valid-scope->ord$inline x)
                  (valid-scope->ord$inline x-equiv)))
  :rule-classes :congruence)