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Representation-of-integer-operations

Shl-ulong-uchar

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

Definitions and Theorems

Function: shl-ulong-uchar

(defun shl-ulong-uchar (x y)
  (declare (xargs :guard (and (ulongp x)
                              (ucharp y)
                              (shl-ulong-uchar-okp x y))))
  (shl-ulong x (integer-from-uchar y)))

Theorem: ulongp-of-shl-ulong-uchar

(defthm ulongp-of-shl-ulong-uchar
  (ulongp (shl-ulong-uchar x y)))

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

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

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

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

Theorem: shl-ulong-uchar-of-uchar-fix-y

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

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

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