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Representation-of-integer-operations

Ge-ullong-schar

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

Definitions and Theorems

Function: ge-ullong-schar

(defun ge-ullong-schar (x y)
  (declare (xargs :guard (and (ullongp x) (scharp y))))
  (ge-ullong-ullong x (ullong-from-schar y)))

Theorem: sintp-of-ge-ullong-schar

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

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

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

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

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

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

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

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

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