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Representation-of-integer-operations

Sub-schar-schar

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

Definitions and Theorems

Function: sub-schar-schar

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

Theorem: sintp-of-sub-schar-schar

(defthm sintp-of-sub-schar-schar
  (sintp (sub-schar-schar x y)))

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

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

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

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

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

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

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

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