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Representation-of-integer-operations

Add-slong-sshort

Addition of a value of type signed long and a value of type signed short [C:6.5.6].

Definitions and Theorems

Function: add-slong-sshort

(defun add-slong-sshort (x y)
  (declare (xargs :guard (and (slongp x)
                              (sshortp y)
                              (add-slong-sshort-okp x y))))
  (add-slong-slong x (slong-from-sshort y)))

Theorem: slongp-of-add-slong-sshort

(defthm slongp-of-add-slong-sshort
  (slongp (add-slong-sshort x y)))

Theorem: add-slong-sshort-of-slong-fix-x

(defthm add-slong-sshort-of-slong-fix-x
  (equal (add-slong-sshort (slong-fix x) y)
         (add-slong-sshort x y)))

Theorem: add-slong-sshort-slong-equiv-congruence-on-x

(defthm add-slong-sshort-slong-equiv-congruence-on-x
  (implies (slong-equiv x x-equiv)
           (equal (add-slong-sshort x y)
                  (add-slong-sshort x-equiv y)))
  :rule-classes :congruence)

Theorem: add-slong-sshort-of-sshort-fix-y

(defthm add-slong-sshort-of-sshort-fix-y
  (equal (add-slong-sshort x (sshort-fix y))
         (add-slong-sshort x y)))

Theorem: add-slong-sshort-sshort-equiv-congruence-on-y

(defthm add-slong-sshort-sshort-equiv-congruence-on-y
  (implies (sshort-equiv y y-equiv)
           (equal (add-slong-sshort x y)
                  (add-slong-sshort x y-equiv)))
  :rule-classes :congruence)