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Representation-of-integer-operations

Shr-sllong-ullong

Right shift of a value of type signed long long and a value of type unsigned long long [C:6.5.7].

Definitions and Theorems

Function: shr-sllong-ullong

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

Theorem: sllongp-of-shr-sllong-ullong

(defthm sllongp-of-shr-sllong-ullong
  (sllongp (shr-sllong-ullong x y)))

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

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

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

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

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

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

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

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