		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Shl-uchar

Left shift of a value of type unsigned char by an integer [C:6.5.7].

Definitions and Theorems

Function: shl-uchar

(defun shl-uchar (x y)
  (declare (xargs :guard (and (ucharp x)
                              (integerp y)
                              (shl-uchar-okp x y))))
  (shl-sint (sint-from-uchar x) y))

Theorem: sintp-of-shl-uchar

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

Theorem: shl-uchar-of-uchar-fix-x

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

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

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

Theorem: shl-uchar-of-ifix-y

(defthm shl-uchar-of-ifix-y
  (equal (shl-uchar x (ifix y))
         (shl-uchar x y)))

Theorem: shl-uchar-int-equiv-congruence-on-y

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