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Coordinate-explicit

Coordinate-explicit->get

Get the get field from a coordinate-explicit.

Signature
(coordinate-explicit->get x) → get
Arguments: x — Guard (coordinatep x).
Returns: get — Type (integerp get).

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

Definitions and Theorems

Function: coordinate-explicit->get$inline

(defun coordinate-explicit->get$inline (x)
  (declare (xargs :guard (coordinatep x)))
  (declare (xargs :guard (equal (coordinate-kind x) :explicit)))
  (let ((__function__ 'coordinate-explicit->get))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (coordinate-kind x) :explicit)
                      x)))
           (ifix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: integerp-of-coordinate-explicit->get

(defthm integerp-of-coordinate-explicit->get
  (b* ((get (coordinate-explicit->get$inline x)))
    (integerp get))
  :rule-classes :rewrite)

Theorem: coordinate-explicit->get$inline-of-coordinate-fix-x

(defthm coordinate-explicit->get$inline-of-coordinate-fix-x
  (equal (coordinate-explicit->get$inline (coordinate-fix x))
         (coordinate-explicit->get$inline x)))

Theorem: coordinate-explicit->get$inline-coordinate-equiv-congruence-on-x

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

Theorem: coordinate-explicit->get-when-wrong-kind

(defthm coordinate-explicit->get-when-wrong-kind
  (implies (not (equal (coordinate-kind x) :explicit))
           (equal (coordinate-explicit->get x)
                  (ifix nil))))