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Smtlink-hint

Smtlink-hint->let-binding

Get the let-binding field from a smtlink-hint.

Signature
(smtlink-hint->let-binding x) → let-binding
Arguments: x — Guard (smtlink-hint-p x).
Returns: let-binding — Type (let-binding-p let-binding).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: smtlink-hint->let-binding$inline

(defun smtlink-hint->let-binding$inline (x)
  (declare (xargs :guard (smtlink-hint-p x)))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'smtlink-hint->let-binding))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((x (and t x)))
           (let-binding-fix (cdr (std::da-nth 3 x))))
         :exec (cdr (std::da-nth 3 x)))))

Theorem: let-binding-p-of-smtlink-hint->let-binding

(defthm let-binding-p-of-smtlink-hint->let-binding
  (b* ((let-binding (smtlink-hint->let-binding$inline x)))
    (let-binding-p let-binding))
  :rule-classes :rewrite)

Theorem: smtlink-hint->let-binding$inline-of-smtlink-hint-fix-x

(defthm smtlink-hint->let-binding$inline-of-smtlink-hint-fix-x
  (equal (smtlink-hint->let-binding$inline (smtlink-hint-fix x))
         (smtlink-hint->let-binding$inline x)))

Theorem: smtlink-hint->let-binding$inline-smtlink-hint-equiv-congruence-on-x

(defthm
 smtlink-hint->let-binding$inline-smtlink-hint-equiv-congruence-on-x
 (implies (smtlink-hint-equiv x x-equiv)
          (equal (smtlink-hint->let-binding$inline x)
                 (smtlink-hint->let-binding$inline x-equiv)))
 :rule-classes :congruence)