Left shift of a value of type
Function:
(defun shl-ulong-slong (x y) (declare (xargs :guard (and (ulongp x) (slongp y) (shl-ulong-slong-okp x y)))) (shl-ulong x (integer-from-slong y)))
Theorem:
(defthm ulongp-of-shl-ulong-slong (ulongp (shl-ulong-slong x y)))
Theorem:
(defthm shl-ulong-slong-of-ulong-fix-x (equal (shl-ulong-slong (ulong-fix x) y) (shl-ulong-slong x y)))
Theorem:
(defthm shl-ulong-slong-ulong-equiv-congruence-on-x (implies (ulong-equiv x x-equiv) (equal (shl-ulong-slong x y) (shl-ulong-slong x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm shl-ulong-slong-of-slong-fix-y (equal (shl-ulong-slong x (slong-fix y)) (shl-ulong-slong x y)))
Theorem:
(defthm shl-ulong-slong-slong-equiv-congruence-on-y (implies (slong-equiv y y-equiv) (equal (shl-ulong-slong x y) (shl-ulong-slong x y-equiv))) :rule-classes :congruence)