Division of a value of type
Function:
(defun div-uchar-schar (x y) (declare (xargs :guard (and (ucharp x) (scharp y) (div-uchar-schar-okp x y)))) (div-sint-sint (sint-from-uchar x) (sint-from-schar y)))
Theorem:
(defthm sintp-of-div-uchar-schar (sintp (div-uchar-schar x y)))
Theorem:
(defthm div-uchar-schar-of-uchar-fix-x (equal (div-uchar-schar (uchar-fix x) y) (div-uchar-schar x y)))
Theorem:
(defthm div-uchar-schar-uchar-equiv-congruence-on-x (implies (uchar-equiv x x-equiv) (equal (div-uchar-schar x y) (div-uchar-schar x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm div-uchar-schar-of-schar-fix-y (equal (div-uchar-schar x (schar-fix y)) (div-uchar-schar x y)))
Theorem:
(defthm div-uchar-schar-schar-equiv-congruence-on-y (implies (schar-equiv y y-equiv) (equal (div-uchar-schar x y) (div-uchar-schar x y-equiv))) :rule-classes :congruence)