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Representation-of-integer-operations

Sub-sllong-uchar

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

Definitions and Theorems

Function: sub-sllong-uchar

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

Theorem: sllongp-of-sub-sllong-uchar

(defthm sllongp-of-sub-sllong-uchar
  (sllongp (sub-sllong-uchar x y)))

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

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

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

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

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

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

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

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