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Representation-of-integer-operations

Sub-ushort-sshort-okp

Check if the subtraction of a value of type unsigned short and a value of type signed short is well-defined.

Definitions and Theorems

Function: sub-ushort-sshort-okp

(defun sub-ushort-sshort-okp (x y)
  (declare (xargs :guard (and (ushortp x) (sshortp y))))
  (sub-sint-sint-okp (sint-from-ushort x)
                     (sint-from-sshort y)))

Theorem: booleanp-of-sub-ushort-sshort-okp

(defthm booleanp-of-sub-ushort-sshort-okp
  (booleanp (sub-ushort-sshort-okp x y)))

Theorem: sub-ushort-sshort-okp-of-ushort-fix-x

(defthm sub-ushort-sshort-okp-of-ushort-fix-x
  (equal (sub-ushort-sshort-okp (ushort-fix x) y)
         (sub-ushort-sshort-okp x y)))

Theorem: sub-ushort-sshort-okp-ushort-equiv-congruence-on-x

(defthm sub-ushort-sshort-okp-ushort-equiv-congruence-on-x
  (implies (ushort-equiv x x-equiv)
           (equal (sub-ushort-sshort-okp x y)
                  (sub-ushort-sshort-okp x-equiv y)))
  :rule-classes :congruence)

Theorem: sub-ushort-sshort-okp-of-sshort-fix-y

(defthm sub-ushort-sshort-okp-of-sshort-fix-y
  (equal (sub-ushort-sshort-okp x (sshort-fix y))
         (sub-ushort-sshort-okp x y)))

Theorem: sub-ushort-sshort-okp-sshort-equiv-congruence-on-y

(defthm sub-ushort-sshort-okp-sshort-equiv-congruence-on-y
  (implies (sshort-equiv y y-equiv)
           (equal (sub-ushort-sshort-okp x y)
                  (sub-ushort-sshort-okp x y-equiv)))
  :rule-classes :congruence)