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Representation-of-integer-operations

Shl-sint-okp

Check if the left shift of a value of type signed int by an integer is well-defined.

Definitions and Theorems

Function: shl-sint-okp

(defun shl-sint-okp (x y)
  (declare (xargs :guard (and (sintp x) (integerp y))))
  (and (integer-range-p 0 (int-bits) (ifix y))
       (>= (integer-from-sint x) 0)
       (sint-integerp (* (integer-from-sint x)
                         (expt 2 (ifix y))))))

Theorem: booleanp-of-shl-sint-okp

(defthm booleanp-of-shl-sint-okp
  (booleanp (shl-sint-okp x y)))

Theorem: shl-sint-okp-of-sint-fix-x

(defthm shl-sint-okp-of-sint-fix-x
  (equal (shl-sint-okp (sint-fix x) y)
         (shl-sint-okp x y)))

Theorem: shl-sint-okp-sint-equiv-congruence-on-x

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

Theorem: shl-sint-okp-of-ifix-y

(defthm shl-sint-okp-of-ifix-y
  (equal (shl-sint-okp x (ifix y))
         (shl-sint-okp x y)))

Theorem: shl-sint-okp-int-equiv-congruence-on-y

(defthm shl-sint-okp-int-equiv-congruence-on-y
  (implies (acl2::int-equiv y y-equiv)
           (equal (shl-sint-okp x y)
                  (shl-sint-okp x y-equiv)))
  :rule-classes :congruence)