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Representation-of-integer-operations

Shl-ushort-ushort

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

Definitions and Theorems

Function: shl-ushort-ushort

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

Theorem: sintp-of-shl-ushort-ushort

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

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

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

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

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

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

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

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

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