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Representation-of-integer-operations

Minus-sshort-okp

Check if the unary minus of a value of type signed short is well-defined.

Definitions and Theorems

Function: minus-sshort-okp

(defun minus-sshort-okp (x)
  (declare (xargs :guard (and (sshortp x))))
  (minus-sint-okp (sint-from-sshort x)))

Theorem: booleanp-of-minus-sshort-okp

(defthm booleanp-of-minus-sshort-okp
  (booleanp (minus-sshort-okp x)))

Theorem: minus-sshort-okp-of-sshort-fix-x

(defthm minus-sshort-okp-of-sshort-fix-x
  (equal (minus-sshort-okp (sshort-fix x))
         (minus-sshort-okp x)))

Theorem: minus-sshort-okp-sshort-equiv-congruence-on-x

(defthm minus-sshort-okp-sshort-equiv-congruence-on-x
  (implies (sshort-equiv x x-equiv)
           (equal (minus-sshort-okp x)
                  (minus-sshort-okp x-equiv)))
  :rule-classes :congruence)