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Representation-of-integer-operations

Sub-ulong-slong

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

Definitions and Theorems

Function: sub-ulong-slong

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

Theorem: ulongp-of-sub-ulong-slong

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

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

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

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

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

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

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

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

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