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Pnumber-number-locase-e-sign

Pnumber-number-locase-e-sign->sign

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

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

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

Definitions and Theorems

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

(defun pnumber-number-locase-e-sign->sign$inline (x)
  (declare (xargs :guard (pnumberp x)))
  (declare (xargs :guard (equal (pnumber-kind x)
                                :number-locase-e-sign)))
  (mbe :logic
       (b* ((x (and (equal (pnumber-kind x)
                           :number-locase-e-sign)
                    x)))
         (sign-fix (std::da-nth 1 (cdr x))))
       :exec (std::da-nth 1 (cdr x))))

Theorem: signp-of-pnumber-number-locase-e-sign->sign

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

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

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

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

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

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

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