		Search-engine friendly clone of the ACL2 documentation.

Fhg-single-args

Fhg-single-args->fn

Get the fn field from a fhg-single-args.

Signature
(fhg-single-args->fn x) → fn
Arguments: x — Guard (fhg-single-args-p x).
Returns: fn — Type (func-p fn).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: fhg-single-args->fn$inline

(defun fhg-single-args->fn$inline (x)
  (declare (xargs :guard (fhg-single-args-p x)))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'fhg-single-args->fn))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((x (and t x)))
           (func-fix (cdr (std::da-nth 0 x))))
         :exec (cdr (std::da-nth 0 x)))))

Theorem: func-p-of-fhg-single-args->fn

(defthm func-p-of-fhg-single-args->fn
  (b* ((fn (fhg-single-args->fn$inline x)))
    (func-p fn))
  :rule-classes :rewrite)

Theorem: fhg-single-args->fn$inline-of-fhg-single-args-fix-x

(defthm fhg-single-args->fn$inline-of-fhg-single-args-fix-x
  (equal (fhg-single-args->fn$inline (fhg-single-args-fix x))
         (fhg-single-args->fn$inline x)))

Theorem: fhg-single-args->fn$inline-fhg-single-args-equiv-congruence-on-x

(defthm
   fhg-single-args->fn$inline-fhg-single-args-equiv-congruence-on-x
  (implies (fhg-single-args-equiv x x-equiv)
           (equal (fhg-single-args->fn$inline x)
                  (fhg-single-args->fn$inline x-equiv)))
  :rule-classes :congruence)