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Representation-of-integer-operations

Gt-slong-uint

Greater-than relation of a value of type signed long and a value of type unsigned int [C17:6.5.8].

Definitions and Theorems

Function: gt-slong-uint

(defun gt-slong-uint (x y)
  (declare (xargs :guard (and (slongp x) (uintp y))))
  (gt-slong-slong x (slong-from-uint y)))

Theorem: sintp-of-gt-slong-uint

(defthm sintp-of-gt-slong-uint
  (sintp (gt-slong-uint x y)))

Theorem: gt-slong-uint-of-slong-fix-x

(defthm gt-slong-uint-of-slong-fix-x
  (equal (gt-slong-uint (slong-fix x) y)
         (gt-slong-uint x y)))

Theorem: gt-slong-uint-slong-equiv-congruence-on-x

(defthm gt-slong-uint-slong-equiv-congruence-on-x
  (implies (slong-equiv x x-equiv)
           (equal (gt-slong-uint x y)
                  (gt-slong-uint x-equiv y)))
  :rule-classes :congruence)

Theorem: gt-slong-uint-of-uint-fix-y

(defthm gt-slong-uint-of-uint-fix-y
  (equal (gt-slong-uint x (uint-fix y))
         (gt-slong-uint x y)))

Theorem: gt-slong-uint-uint-equiv-congruence-on-y

(defthm gt-slong-uint-uint-equiv-congruence-on-y
  (implies (uint-equiv y y-equiv)
           (equal (gt-slong-uint x y)
                  (gt-slong-uint x y-equiv)))
  :rule-classes :congruence)