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