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Representation-of-integer-operations

Sub-schar-slong

Subtraction of a value of type signed char and a value of type signed long [C17:6.5.6].

Definitions and Theorems

Function: sub-schar-slong

(defun sub-schar-slong (x y)
  (declare (xargs :guard (and (scharp x)
                              (slongp y)
                              (sub-schar-slong-okp x y))))
  (sub-slong-slong (slong-from-schar x)
                   y))

Theorem: slongp-of-sub-schar-slong

(defthm slongp-of-sub-schar-slong
  (slongp (sub-schar-slong x y)))

Theorem: sub-schar-slong-of-schar-fix-x

(defthm sub-schar-slong-of-schar-fix-x
  (equal (sub-schar-slong (schar-fix x) y)
         (sub-schar-slong x y)))

Theorem: sub-schar-slong-schar-equiv-congruence-on-x

(defthm sub-schar-slong-schar-equiv-congruence-on-x
  (implies (schar-equiv x x-equiv)
           (equal (sub-schar-slong x y)
                  (sub-schar-slong x-equiv y)))
  :rule-classes :congruence)

Theorem: sub-schar-slong-of-slong-fix-y

(defthm sub-schar-slong-of-slong-fix-y
  (equal (sub-schar-slong x (slong-fix y))
         (sub-schar-slong x y)))

Theorem: sub-schar-slong-slong-equiv-congruence-on-y

(defthm sub-schar-slong-slong-equiv-congruence-on-y
  (implies (slong-equiv y y-equiv)
           (equal (sub-schar-slong x y)
                  (sub-schar-slong x y-equiv)))
  :rule-classes :congruence)