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Representation-of-integer-operations

Sub-ullong-sint

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

Definitions and Theorems

Function: sub-ullong-sint

(defun sub-ullong-sint (x y)
  (declare (xargs :guard (and (ullongp x) (sintp y))))
  (sub-ullong-ullong x (ullong-from-sint y)))

Theorem: ullongp-of-sub-ullong-sint

(defthm ullongp-of-sub-ullong-sint
  (ullongp (sub-ullong-sint x y)))

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

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

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

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

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

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

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

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