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Representation-of-integer-operations

Sub-sint-uint

Subtraction of a value of type signed int and a value of type unsigned int [C:6.5.6].

Definitions and Theorems

Function: sub-sint-uint

(defun sub-sint-uint (x y)
  (declare (xargs :guard (and (sintp x) (uintp y))))
  (sub-uint-uint (uint-from-sint x) y))

Theorem: uintp-of-sub-sint-uint

(defthm uintp-of-sub-sint-uint
  (uintp (sub-sint-uint x y)))

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

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

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

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

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

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

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

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