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Check if the addition of a value of type
Function:
(defun add-slong-slong-okp (x y) (declare (xargs :guard (and (slongp x) (slongp y)))) (slong-integerp (+ (integer-from-slong x) (integer-from-slong y))))
Theorem:
(defthm booleanp-of-add-slong-slong-okp (booleanp (add-slong-slong-okp x y)))
Theorem:
(defthm add-slong-slong-okp-of-slong-fix-x (equal (add-slong-slong-okp (slong-fix x) y) (add-slong-slong-okp x y)))
Theorem:
(defthm add-slong-slong-okp-slong-equiv-congruence-on-x (implies (slong-equiv x x-equiv) (equal (add-slong-slong-okp x y) (add-slong-slong-okp x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm add-slong-slong-okp-of-slong-fix-y (equal (add-slong-slong-okp x (slong-fix y)) (add-slong-slong-okp x y)))
Theorem:
(defthm add-slong-slong-okp-slong-equiv-congruence-on-y (implies (slong-equiv y y-equiv) (equal (add-slong-slong-okp x y) (add-slong-slong-okp x y-equiv))) :rule-classes :congruence)