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Sinteger-bit-role-value

Sinteger-bit-role-value->exp

Get the exp field from a sinteger-bit-role-value.

Signature
(sinteger-bit-role-value->exp x) → exp
Arguments: x — Guard (sinteger-bit-rolep x).
Returns: exp — Type (natp exp).

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

Definitions and Theorems

Function: sinteger-bit-role-value->exp$inline

(defun sinteger-bit-role-value->exp$inline (x)
  (declare (xargs :guard (sinteger-bit-rolep x)))
  (declare (xargs :guard (equal (sinteger-bit-role-kind x)
                                :value)))
  (mbe :logic
       (b* ((x (and (equal (sinteger-bit-role-kind x)
                           :value)
                    x)))
         (nfix (std::da-nth 0 (cdr x))))
       :exec (std::da-nth 0 (cdr x))))

Theorem: natp-of-sinteger-bit-role-value->exp

(defthm natp-of-sinteger-bit-role-value->exp
  (b* ((exp (sinteger-bit-role-value->exp$inline x)))
    (natp exp))
  :rule-classes :rewrite)

Theorem: sinteger-bit-role-value->exp$inline-of-sinteger-bit-role-fix-x

(defthm
     sinteger-bit-role-value->exp$inline-of-sinteger-bit-role-fix-x
 (equal
     (sinteger-bit-role-value->exp$inline (sinteger-bit-role-fix x))
     (sinteger-bit-role-value->exp$inline x)))

Theorem: sinteger-bit-role-value->exp$inline-sinteger-bit-role-equiv-congruence-on-x

(defthm
 sinteger-bit-role-value->exp$inline-sinteger-bit-role-equiv-congruence-on-x
 (implies (sinteger-bit-role-equiv x x-equiv)
          (equal (sinteger-bit-role-value->exp$inline x)
                 (sinteger-bit-role-value->exp$inline x-equiv)))
 :rule-classes :congruence)

Theorem: sinteger-bit-role-value->exp-when-wrong-kind

(defthm sinteger-bit-role-value->exp-when-wrong-kind
  (implies (not (equal (sinteger-bit-role-kind x)
                       :value))
           (equal (sinteger-bit-role-value->exp x)
                  (nfix nil))))