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Representation-of-integer-operations

Sub-sint-sint-okp

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

Definitions and Theorems

Function: sub-sint-sint-okp

(defun sub-sint-sint-okp (x y)
  (declare (xargs :guard (and (sintp x) (sintp y))))
  (sint-integerp (- (integer-from-sint x)
                    (integer-from-sint y))))

Theorem: booleanp-of-sub-sint-sint-okp

(defthm booleanp-of-sub-sint-sint-okp
  (booleanp (sub-sint-sint-okp x y)))

Theorem: sub-sint-sint-okp-of-sint-fix-x

(defthm sub-sint-sint-okp-of-sint-fix-x
  (equal (sub-sint-sint-okp (sint-fix x) y)
         (sub-sint-sint-okp x y)))

Theorem: sub-sint-sint-okp-sint-equiv-congruence-on-x

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

Theorem: sub-sint-sint-okp-of-sint-fix-y

(defthm sub-sint-sint-okp-of-sint-fix-y
  (equal (sub-sint-sint-okp x (sint-fix y))
         (sub-sint-sint-okp x y)))

Theorem: sub-sint-sint-okp-sint-equiv-congruence-on-y

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