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Representation-of-integer-operations

Sub-ullong-uint

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

Definitions and Theorems

Function: sub-ullong-uint

(defun sub-ullong-uint (x y)
  (declare (xargs :guard (and (ullongp x) (uintp y))))
  (sub-ullong-ullong x (ullong-from-uint y)))

Theorem: ullongp-of-sub-ullong-uint

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

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

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

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

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

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

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

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

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