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Func

Func->guard

Get the guard field from a func.

Signature
(func->guard x) → guard
Arguments: x — Guard (func-p x).
Returns: guard — Type (hint-pair-p guard).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: func->guard$inline

(defun func->guard$inline (x)
  (declare (xargs :guard (func-p x)))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'func->guard))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((x (and t x)))
           (hint-pair-fix (cdr (std::da-nth 2 x))))
         :exec (cdr (std::da-nth 2 x)))))

Theorem: hint-pair-p-of-func->guard

(defthm hint-pair-p-of-func->guard
  (b* ((guard (func->guard$inline x)))
    (hint-pair-p guard))
  :rule-classes :rewrite)

Theorem: func->guard$inline-of-func-fix-x

(defthm func->guard$inline-of-func-fix-x
  (equal (func->guard$inline (func-fix x))
         (func->guard$inline x)))

Theorem: func->guard$inline-func-equiv-congruence-on-x

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