Check if the left shift of a value of type
Function:
(defun shl-ulong-sint-okp (x y) (declare (xargs :guard (and (ulongp x) (sintp y)))) (shl-ulong-okp x (integer-from-sint y)))
Theorem:
(defthm booleanp-of-shl-ulong-sint-okp (booleanp (shl-ulong-sint-okp x y)))
Theorem:
(defthm shl-ulong-sint-okp-of-ulong-fix-x (equal (shl-ulong-sint-okp (ulong-fix x) y) (shl-ulong-sint-okp x y)))
Theorem:
(defthm shl-ulong-sint-okp-ulong-equiv-congruence-on-x (implies (ulong-equiv x x-equiv) (equal (shl-ulong-sint-okp x y) (shl-ulong-sint-okp x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm shl-ulong-sint-okp-of-sint-fix-y (equal (shl-ulong-sint-okp x (sint-fix y)) (shl-ulong-sint-okp x y)))
Theorem:
(defthm shl-ulong-sint-okp-sint-equiv-congruence-on-y (implies (sint-equiv y y-equiv) (equal (shl-ulong-sint-okp x y) (shl-ulong-sint-okp x y-equiv))) :rule-classes :congruence)