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Programdef-mapping

Programdef-mapping->get

Get the get field from a programdef-mapping.

Signature
(programdef-mapping->get x) → get
Arguments: x — Guard (programdefp x).
Returns: get — Type (mappingp get).

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

Definitions and Theorems

Function: programdef-mapping->get$inline

(defun programdef-mapping->get$inline (x)
  (declare (xargs :guard (programdefp x)))
  (declare (xargs :guard (equal (programdef-kind x) :mapping)))
  (let ((__function__ 'programdef-mapping->get))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (programdef-kind x) :mapping)
                      x)))
           (mapping-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: mappingp-of-programdef-mapping->get

(defthm mappingp-of-programdef-mapping->get
  (b* ((get (programdef-mapping->get$inline x)))
    (mappingp get))
  :rule-classes :rewrite)

Theorem: programdef-mapping->get$inline-of-programdef-fix-x

(defthm programdef-mapping->get$inline-of-programdef-fix-x
  (equal (programdef-mapping->get$inline (programdef-fix x))
         (programdef-mapping->get$inline x)))

Theorem: programdef-mapping->get$inline-programdef-equiv-congruence-on-x

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

Theorem: programdef-mapping->get-when-wrong-kind

(defthm programdef-mapping->get-when-wrong-kind
  (implies (not (equal (programdef-kind x) :mapping))
           (equal (programdef-mapping->get x)
                  (mapping-fix nil))))