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Representation-of-integer-operations

Ge-ushort-schar

Greater-than-or-equal-to relation of a value of type unsigned short and a value of type signed char [C:6.5.8].

Definitions and Theorems

Function: ge-ushort-schar

(defun ge-ushort-schar (x y)
  (declare (xargs :guard (and (ushortp x) (scharp y))))
  (ge-sint-sint (sint-from-ushort x)
                (sint-from-schar y)))

Theorem: sintp-of-ge-ushort-schar

(defthm sintp-of-ge-ushort-schar
  (sintp (ge-ushort-schar x y)))

Theorem: ge-ushort-schar-of-ushort-fix-x

(defthm ge-ushort-schar-of-ushort-fix-x
  (equal (ge-ushort-schar (ushort-fix x) y)
         (ge-ushort-schar x y)))

Theorem: ge-ushort-schar-ushort-equiv-congruence-on-x

(defthm ge-ushort-schar-ushort-equiv-congruence-on-x
  (implies (ushort-equiv x x-equiv)
           (equal (ge-ushort-schar x y)
                  (ge-ushort-schar x-equiv y)))
  :rule-classes :congruence)

Theorem: ge-ushort-schar-of-schar-fix-y

(defthm ge-ushort-schar-of-schar-fix-y
  (equal (ge-ushort-schar x (schar-fix y))
         (ge-ushort-schar x y)))

Theorem: ge-ushort-schar-schar-equiv-congruence-on-y

(defthm ge-ushort-schar-schar-equiv-congruence-on-y
  (implies (schar-equiv y y-equiv)
           (equal (ge-ushort-schar x y)
                  (ge-ushort-schar x y-equiv)))
  :rule-classes :congruence)