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Representation-of-integer-operations

Sub-sllong-sllong-okp

Check if the subtraction of a value of type signed long long and a value of type signed long long is well-defined.

Definitions and Theorems

Function: sub-sllong-sllong-okp

(defun sub-sllong-sllong-okp (x y)
  (declare (xargs :guard (and (sllongp x) (sllongp y))))
  (sllong-integerp (- (integer-from-sllong x)
                      (integer-from-sllong y))))

Theorem: booleanp-of-sub-sllong-sllong-okp

(defthm booleanp-of-sub-sllong-sllong-okp
  (booleanp (sub-sllong-sllong-okp x y)))

Theorem: sub-sllong-sllong-okp-of-sllong-fix-x

(defthm sub-sllong-sllong-okp-of-sllong-fix-x
  (equal (sub-sllong-sllong-okp (sllong-fix x) y)
         (sub-sllong-sllong-okp x y)))

Theorem: sub-sllong-sllong-okp-sllong-equiv-congruence-on-x

(defthm sub-sllong-sllong-okp-sllong-equiv-congruence-on-x
  (implies (sllong-equiv x x-equiv)
           (equal (sub-sllong-sllong-okp x y)
                  (sub-sllong-sllong-okp x-equiv y)))
  :rule-classes :congruence)

Theorem: sub-sllong-sllong-okp-of-sllong-fix-y

(defthm sub-sllong-sllong-okp-of-sllong-fix-y
  (equal (sub-sllong-sllong-okp x (sllong-fix y))
         (sub-sllong-sllong-okp x y)))

Theorem: sub-sllong-sllong-okp-sllong-equiv-congruence-on-y

(defthm sub-sllong-sllong-okp-sllong-equiv-congruence-on-y
  (implies (sllong-equiv y y-equiv)
           (equal (sub-sllong-sllong-okp x y)
                  (sub-sllong-sllong-okp x y-equiv)))
  :rule-classes :congruence)