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Sparseint$-leaf

Sparseint$-leaf->val

Get the val field from a sparseint$-leaf.

Signature
(sparseint$-leaf->val x) → val
Arguments: x — Guard (sparseint$-p x).
Returns: val — Type (integerp val).

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

Definitions and Theorems

Function: sparseint$-leaf->val$inline

(defun sparseint$-leaf->val$inline (x)
  (declare (xargs :guard (sparseint$-p x)))
  (declare (xargs :guard (equal (sparseint$-kind x) :leaf)))
  (let ((__function__ 'sparseint$-leaf->val))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (sparseint$-kind x) :leaf)
                      x)))
           (ifix x))
         :exec x)))

Theorem: integerp-of-sparseint$-leaf->val

(defthm integerp-of-sparseint$-leaf->val
  (b* ((val (sparseint$-leaf->val$inline x)))
    (integerp val))
  :rule-classes :type-prescription)

Theorem: sparseint$-leaf->val$inline-of-sparseint$-fix-x

(defthm sparseint$-leaf->val$inline-of-sparseint$-fix-x
  (equal (sparseint$-leaf->val$inline (sparseint$-fix x))
         (sparseint$-leaf->val$inline x)))

Theorem: sparseint$-leaf->val$inline-sparseint$-equiv-congruence-on-x

(defthm sparseint$-leaf->val$inline-sparseint$-equiv-congruence-on-x
  (implies (sparseint$-equiv x x-equiv)
           (equal (sparseint$-leaf->val$inline x)
                  (sparseint$-leaf->val$inline x-equiv)))
  :rule-classes :congruence)

Theorem: sparseint$-leaf->val-when-wrong-kind

(defthm sparseint$-leaf->val-when-wrong-kind
  (implies (not (equal (sparseint$-kind x) :leaf))
           (equal (sparseint$-leaf->val x)
                  (ifix nil))))