		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Shl-ushort-ulong

Left shift of a value of type unsigned short and a value of type unsigned long [C17:6.5.7].

Definitions and Theorems

Function: shl-ushort-ulong

(defun shl-ushort-ulong (x y)
  (declare (xargs :guard (and (ushortp x)
                              (ulongp y)
                              (shl-ushort-ulong-okp x y))))
  (shl-ushort x (integer-from-ulong y)))

Theorem: sintp-of-shl-ushort-ulong

(defthm sintp-of-shl-ushort-ulong
  (sintp (shl-ushort-ulong x y)))

Theorem: shl-ushort-ulong-of-ushort-fix-x

(defthm shl-ushort-ulong-of-ushort-fix-x
  (equal (shl-ushort-ulong (ushort-fix x) y)
         (shl-ushort-ulong x y)))

Theorem: shl-ushort-ulong-ushort-equiv-congruence-on-x

(defthm shl-ushort-ulong-ushort-equiv-congruence-on-x
  (implies (ushort-equiv x x-equiv)
           (equal (shl-ushort-ulong x y)
                  (shl-ushort-ulong x-equiv y)))
  :rule-classes :congruence)

Theorem: shl-ushort-ulong-of-ulong-fix-y

(defthm shl-ushort-ulong-of-ulong-fix-y
  (equal (shl-ushort-ulong x (ulong-fix y))
         (shl-ushort-ulong x y)))

Theorem: shl-ushort-ulong-ulong-equiv-congruence-on-y

(defthm shl-ushort-ulong-ulong-equiv-congruence-on-y
  (implies (ulong-equiv y y-equiv)
           (equal (shl-ushort-ulong x y)
                  (shl-ushort-ulong x y-equiv)))
  :rule-classes :congruence)