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Representation-of-integer-operations

Add-sshort-schar-okp

Check if the addition of a value of type signed short and a value of type signed char is well-defined.

Definitions and Theorems

Function: add-sshort-schar-okp

(defun add-sshort-schar-okp (x y)
  (declare (xargs :guard (and (sshortp x) (scharp y))))
  (add-sint-sint-okp (sint-from-sshort x)
                     (sint-from-schar y)))

Theorem: booleanp-of-add-sshort-schar-okp

(defthm booleanp-of-add-sshort-schar-okp
  (booleanp (add-sshort-schar-okp x y)))

Theorem: add-sshort-schar-okp-of-sshort-fix-x

(defthm add-sshort-schar-okp-of-sshort-fix-x
  (equal (add-sshort-schar-okp (sshort-fix x) y)
         (add-sshort-schar-okp x y)))

Theorem: add-sshort-schar-okp-sshort-equiv-congruence-on-x

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

Theorem: add-sshort-schar-okp-of-schar-fix-y

(defthm add-sshort-schar-okp-of-schar-fix-y
  (equal (add-sshort-schar-okp x (schar-fix y))
         (add-sshort-schar-okp x y)))

Theorem: add-sshort-schar-okp-schar-equiv-congruence-on-y

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