Subtraction of a value of type
Function:
(defun sub-sint-sint (x y) (declare (xargs :guard (and (sintp x) (sintp y) (sub-sint-sint-okp x y)))) (sint-from-integer (- (integer-from-sint x) (integer-from-sint y))))
Theorem:
(defthm sintp-of-sub-sint-sint (sintp (sub-sint-sint x y)))
Theorem:
(defthm sub-sint-sint-of-sint-fix-x (equal (sub-sint-sint (sint-fix x) y) (sub-sint-sint x y)))
Theorem:
(defthm sub-sint-sint-sint-equiv-congruence-on-x (implies (sint-equiv x x-equiv) (equal (sub-sint-sint x y) (sub-sint-sint x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm sub-sint-sint-of-sint-fix-y (equal (sub-sint-sint x (sint-fix y)) (sub-sint-sint x y)))
Theorem:
(defthm sub-sint-sint-sint-equiv-congruence-on-y (implies (sint-equiv y y-equiv) (equal (sub-sint-sint x y) (sub-sint-sint x y-equiv))) :rule-classes :congruence)