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Pnumber-number-upcase-e-sign

Pnumber-number-upcase-e-sign->number

Get the number field from a pnumber-number-upcase-e-sign.

Signature
(pnumber-number-upcase-e-sign->number x) → number
Arguments: x — Guard (pnumberp x).
Returns: number — Type (pnumberp number).

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

Definitions and Theorems

Function: pnumber-number-upcase-e-sign->number$inline

(defun pnumber-number-upcase-e-sign->number$inline (x)
  (declare (xargs :guard (pnumberp x)))
  (declare (xargs :guard (equal (pnumber-kind x)
                                :number-upcase-e-sign)))
  (mbe :logic
       (b* ((x (and (equal (pnumber-kind x)
                           :number-upcase-e-sign)
                    x)))
         (pnumber-fix (std::da-nth 0 (cdr x))))
       :exec (std::da-nth 0 (cdr x))))

Theorem: pnumberp-of-pnumber-number-upcase-e-sign->number

(defthm pnumberp-of-pnumber-number-upcase-e-sign->number
  (b* ((number (pnumber-number-upcase-e-sign->number$inline x)))
    (pnumberp number))
  :rule-classes :rewrite)

Theorem: pnumber-number-upcase-e-sign->number$inline-of-pnumber-fix-x

(defthm pnumber-number-upcase-e-sign->number$inline-of-pnumber-fix-x
  (equal
       (pnumber-number-upcase-e-sign->number$inline (pnumber-fix x))
       (pnumber-number-upcase-e-sign->number$inline x)))

Theorem: pnumber-number-upcase-e-sign->number$inline-pnumber-equiv-congruence-on-x

(defthm
 pnumber-number-upcase-e-sign->number$inline-pnumber-equiv-congruence-on-x
 (implies
      (pnumber-equiv x x-equiv)
      (equal (pnumber-number-upcase-e-sign->number$inline x)
             (pnumber-number-upcase-e-sign->number$inline x-equiv)))
 :rule-classes :congruence)

Theorem: pnumber-number-upcase-e-sign->number-when-wrong-kind

(defthm pnumber-number-upcase-e-sign->number-when-wrong-kind
  (implies (not (equal (pnumber-kind x)
                       :number-upcase-e-sign))
           (equal (pnumber-number-upcase-e-sign->number x)
                  (pnumber-fix nil))))