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Binding

Binding->var

Get the var field from a binding.

Signature
(binding->var x) → var
Arguments: x — Guard (binding-p x).
Returns: var — Type (symbolp var).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: binding->var$inline

(defun binding->var$inline (x)
  (declare (xargs :guard (binding-p x)))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'binding->var))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((x (and t x)))
           (symbol-fix (cdr (std::da-nth 0 x))))
         :exec (cdr (std::da-nth 0 x)))))

Theorem: symbolp-of-binding->var

(defthm symbolp-of-binding->var
  (b* ((var (binding->var$inline x)))
    (symbolp var))
  :rule-classes :rewrite)

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

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

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

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