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Representation-of-integer-operations

Ge-slong-uchar

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

Definitions and Theorems

Function: ge-slong-uchar

(defun ge-slong-uchar (x y)
  (declare (xargs :guard (and (slongp x) (ucharp y))))
  (ge-slong-slong x (slong-from-uchar y)))

Theorem: sintp-of-ge-slong-uchar

(defthm sintp-of-ge-slong-uchar
  (sintp (ge-slong-uchar x y)))

Theorem: ge-slong-uchar-of-slong-fix-x

(defthm ge-slong-uchar-of-slong-fix-x
  (equal (ge-slong-uchar (slong-fix x) y)
         (ge-slong-uchar x y)))

Theorem: ge-slong-uchar-slong-equiv-congruence-on-x

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

Theorem: ge-slong-uchar-of-uchar-fix-y

(defthm ge-slong-uchar-of-uchar-fix-y
  (equal (ge-slong-uchar x (uchar-fix y))
         (ge-slong-uchar x y)))

Theorem: ge-slong-uchar-uchar-equiv-congruence-on-y

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