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Representation-of-integer-operations

Sub-slong-ulong

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

Definitions and Theorems

Function: sub-slong-ulong

(defun sub-slong-ulong (x y)
  (declare (xargs :guard (and (slongp x) (ulongp y))))
  (sub-ulong-ulong (ulong-from-slong x)
                   y))

Theorem: ulongp-of-sub-slong-ulong

(defthm ulongp-of-sub-slong-ulong
  (ulongp (sub-slong-ulong x y)))

Theorem: sub-slong-ulong-of-slong-fix-x

(defthm sub-slong-ulong-of-slong-fix-x
  (equal (sub-slong-ulong (slong-fix x) y)
         (sub-slong-ulong x y)))

Theorem: sub-slong-ulong-slong-equiv-congruence-on-x

(defthm sub-slong-ulong-slong-equiv-congruence-on-x
  (implies (slong-equiv x x-equiv)
           (equal (sub-slong-ulong x y)
                  (sub-slong-ulong x-equiv y)))
  :rule-classes :congruence)

Theorem: sub-slong-ulong-of-ulong-fix-y

(defthm sub-slong-ulong-of-ulong-fix-y
  (equal (sub-slong-ulong x (ulong-fix y))
         (sub-slong-ulong x y)))

Theorem: sub-slong-ulong-ulong-equiv-congruence-on-y

(defthm sub-slong-ulong-ulong-equiv-congruence-on-y
  (implies (ulong-equiv y y-equiv)
           (equal (sub-slong-ulong x y)
                  (sub-slong-ulong x y-equiv)))
  :rule-classes :congruence)