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Sinteger-format

Sinteger-format->signed

Get the signed field from a sinteger-format.

Signature
(sinteger-format->signed x) → signed
Arguments: x — Guard (sinteger-formatp x).
Returns: signed — Type (signed-formatp signed).

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

Definitions and Theorems

Function: sinteger-format->signed$inline

(defun sinteger-format->signed$inline (x)
  (declare (xargs :guard (sinteger-formatp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'sinteger-format->signed))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (signed-format-fix (cdr (std::da-nth 1 x))))
         :exec (cdr (std::da-nth 1 x)))))

Theorem: signed-formatp-of-sinteger-format->signed

(defthm signed-formatp-of-sinteger-format->signed
  (b* ((signed (sinteger-format->signed$inline x)))
    (signed-formatp signed))
  :rule-classes :rewrite)

Theorem: sinteger-format->signed$inline-of-sinteger-format-fix-x

(defthm sinteger-format->signed$inline-of-sinteger-format-fix-x
  (equal (sinteger-format->signed$inline (sinteger-format-fix x))
         (sinteger-format->signed$inline x)))

Theorem: sinteger-format->signed$inline-sinteger-format-equiv-congruence-on-x

(defthm
 sinteger-format->signed$inline-sinteger-format-equiv-congruence-on-x
 (implies (sinteger-format-equiv x x-equiv)
          (equal (sinteger-format->signed$inline x)
                 (sinteger-format->signed$inline x-equiv)))
 :rule-classes :congruence)