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Let-binding

Let-binding->hypotheses

Get the hypotheses field from a let-binding.

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

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: let-binding->hypotheses$inline

(defun let-binding->hypotheses$inline (x)
  (declare (xargs :guard (let-binding-p x)))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'let-binding->hypotheses))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((x (and t x)))
           (hint-pair-list-fix (cdr (std::da-nth 1 x))))
         :exec (cdr (std::da-nth 1 x)))))

Theorem: hint-pair-listp-of-let-binding->hypotheses

(defthm hint-pair-listp-of-let-binding->hypotheses
  (b* ((hypotheses (let-binding->hypotheses$inline x)))
    (hint-pair-listp hypotheses))
  :rule-classes :rewrite)

Theorem: let-binding->hypotheses$inline-of-let-binding-fix-x

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

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

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