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Representation-of-integer-operations

Shl-ushort-uchar

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

Definitions and Theorems

Function: shl-ushort-uchar

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

Theorem: sintp-of-shl-ushort-uchar

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

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

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

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

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

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

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

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

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