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Toplevel-functions

Toplevel-functions->get

Get the get field from a toplevel-functions.

Signature
(toplevel-functions->get x) → get
Arguments: x — Guard (toplevelp x).
Returns: get — Type (function-recursionp get).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: toplevel-functions->get$inline

(defun toplevel-functions->get$inline (x)
  (declare (xargs :guard (toplevelp x)))
  (declare (xargs :guard (equal (toplevel-kind x) :functions)))
  (let ((__function__ 'toplevel-functions->get))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (toplevel-kind x) :functions)
                      x)))
           (function-recursion-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: function-recursionp-of-toplevel-functions->get

(defthm function-recursionp-of-toplevel-functions->get
  (b* ((get (toplevel-functions->get$inline x)))
    (function-recursionp get))
  :rule-classes :rewrite)

Theorem: toplevel-functions->get$inline-of-toplevel-fix-x

(defthm toplevel-functions->get$inline-of-toplevel-fix-x
  (equal (toplevel-functions->get$inline (toplevel-fix x))
         (toplevel-functions->get$inline x)))

Theorem: toplevel-functions->get$inline-toplevel-equiv-congruence-on-x

(defthm
      toplevel-functions->get$inline-toplevel-equiv-congruence-on-x
  (implies (toplevel-equiv x x-equiv)
           (equal (toplevel-functions->get$inline x)
                  (toplevel-functions->get$inline x-equiv)))
  :rule-classes :congruence)

Theorem: toplevel-functions->get-when-wrong-kind

(defthm toplevel-functions->get-when-wrong-kind
  (implies (not (equal (toplevel-kind x) :functions))
           (equal (toplevel-functions->get x)
                  (function-recursion-fix nil))))