Subtraction of a value of type
Function:
(defun sub-schar-uint (x y) (declare (xargs :guard (and (scharp x) (uintp y)))) (sub-uint-uint (uint-from-schar x) y))
Theorem:
(defthm uintp-of-sub-schar-uint (uintp (sub-schar-uint x y)))
Theorem:
(defthm sub-schar-uint-of-schar-fix-x (equal (sub-schar-uint (schar-fix x) y) (sub-schar-uint x y)))
Theorem:
(defthm sub-schar-uint-schar-equiv-congruence-on-x (implies (schar-equiv x x-equiv) (equal (sub-schar-uint x y) (sub-schar-uint x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm sub-schar-uint-of-uint-fix-y (equal (sub-schar-uint x (uint-fix y)) (sub-schar-uint x y)))
Theorem:
(defthm sub-schar-uint-uint-equiv-congruence-on-y (implies (uint-equiv y y-equiv) (equal (sub-schar-uint x y) (sub-schar-uint x y-equiv))) :rule-classes :congruence)