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Representation-of-integer-operations

Sub-ushort-uchar

Subtraction of a value of type unsigned short and a value of type unsigned char [C:6.5.6].

Definitions and Theorems

Function: sub-ushort-uchar

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

Theorem: sintp-of-sub-ushort-uchar

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

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

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

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

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

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

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

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

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