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Binding

Binding->expr

Get the expr field from a binding.

Signature
(binding->expr x) → expr
Arguments: x — Guard (binding-p x).
Returns: expr — Type (pseudo-termp expr).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: binding->expr$inline

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

Theorem: pseudo-termp-of-binding->expr

(defthm pseudo-termp-of-binding->expr
  (b* ((expr (binding->expr$inline x)))
    (pseudo-termp expr))
  :rule-classes :rewrite)

Theorem: binding->expr$inline-of-binding-fix-x

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

Theorem: binding->expr$inline-binding-equiv-congruence-on-x

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