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Representation-of-integer-operations

Shr-uint-ushort

Right shift of a value of type unsigned int and a value of type unsigned short [C17:6.5.7].

Definitions and Theorems

Function: shr-uint-ushort

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

Theorem: uintp-of-shr-uint-ushort

(defthm uintp-of-shr-uint-ushort
  (uintp (shr-uint-ushort x y)))

Theorem: shr-uint-ushort-of-uint-fix-x

(defthm shr-uint-ushort-of-uint-fix-x
  (equal (shr-uint-ushort (uint-fix x) y)
         (shr-uint-ushort x y)))

Theorem: shr-uint-ushort-uint-equiv-congruence-on-x

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

Theorem: shr-uint-ushort-of-ushort-fix-y

(defthm shr-uint-ushort-of-ushort-fix-y
  (equal (shr-uint-ushort x (ushort-fix y))
         (shr-uint-ushort x y)))

Theorem: shr-uint-ushort-ushort-equiv-congruence-on-y

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