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Representation-of-integer-operations

Bitand-ullong-sllong

Bitwise conjunction of a value of type unsigned long long and a value of type signed long long [C:6.5.10].

Definitions and Theorems

Function: bitand-ullong-sllong

(defun bitand-ullong-sllong (x y)
  (declare (xargs :guard (and (ullongp x) (sllongp y))))
  (bitand-ullong-ullong x (ullong-from-sllong y)))

Theorem: ullongp-of-bitand-ullong-sllong

(defthm ullongp-of-bitand-ullong-sllong
  (ullongp (bitand-ullong-sllong x y)))

Theorem: bitand-ullong-sllong-of-ullong-fix-x

(defthm bitand-ullong-sllong-of-ullong-fix-x
  (equal (bitand-ullong-sllong (ullong-fix x) y)
         (bitand-ullong-sllong x y)))

Theorem: bitand-ullong-sllong-ullong-equiv-congruence-on-x

(defthm bitand-ullong-sllong-ullong-equiv-congruence-on-x
  (implies (ullong-equiv x x-equiv)
           (equal (bitand-ullong-sllong x y)
                  (bitand-ullong-sllong x-equiv y)))
  :rule-classes :congruence)

Theorem: bitand-ullong-sllong-of-sllong-fix-y

(defthm bitand-ullong-sllong-of-sllong-fix-y
  (equal (bitand-ullong-sllong x (sllong-fix y))
         (bitand-ullong-sllong x y)))

Theorem: bitand-ullong-sllong-sllong-equiv-congruence-on-y

(defthm bitand-ullong-sllong-sllong-equiv-congruence-on-y
  (implies (sllong-equiv y y-equiv)
           (equal (bitand-ullong-sllong x y)
                  (bitand-ullong-sllong x y-equiv)))
  :rule-classes :congruence)