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Representation-of-integer-operations

Shl-uint-uint

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

Definitions and Theorems

Function: shl-uint-uint

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

Theorem: uintp-of-shl-uint-uint

(defthm uintp-of-shl-uint-uint
  (uintp (shl-uint-uint x y)))

Theorem: shl-uint-uint-of-uint-fix-x

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

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

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

Theorem: shl-uint-uint-of-uint-fix-y

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

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

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