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Sparseint$-concat

Sparseint$-concat->msbs

Get the msbs field from a sparseint$-concat.

Signature
(sparseint$-concat->msbs x) → msbs
Arguments: x — Guard (sparseint$-p x).
Returns: msbs — Type (sparseint$-p msbs).

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

Definitions and Theorems

Function: sparseint$-concat->msbs$inline

(defun sparseint$-concat->msbs$inline (x)
  (declare (xargs :guard (sparseint$-p x)))
  (declare (xargs :guard (equal (sparseint$-kind x) :concat)))
  (let ((__function__ 'sparseint$-concat->msbs))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (sparseint$-kind x) :concat)
                      x)))
           (sparseint$-fix (cddr x)))
         :exec (cddr x))))

Theorem: sparseint$-p-of-sparseint$-concat->msbs

(defthm sparseint$-p-of-sparseint$-concat->msbs
  (b* ((msbs (sparseint$-concat->msbs$inline x)))
    (sparseint$-p msbs))
  :rule-classes :rewrite)

Theorem: sparseint$-concat->msbs$inline-of-sparseint$-fix-x

(defthm sparseint$-concat->msbs$inline-of-sparseint$-fix-x
  (equal (sparseint$-concat->msbs$inline (sparseint$-fix x))
         (sparseint$-concat->msbs$inline x)))

Theorem: sparseint$-concat->msbs$inline-sparseint$-equiv-congruence-on-x

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

Theorem: sparseint$-concat->msbs-when-wrong-kind

(defthm sparseint$-concat->msbs-when-wrong-kind
  (implies (not (equal (sparseint$-kind x) :concat))
           (equal (sparseint$-concat->msbs x)
                  (sparseint$-fix nil))))