let V be non empty right_complementable add-associative right_zeroed addLoopStr ; for v, u, w being Element of V holds Sum <*u,v,w*> = (Sum <*u,v*>) + w
let v, u, w be Element of V; Sum <*u,v,w*> = (Sum <*u,v*>) + w
thus Sum <*u,v,w*> =
(u + v) + w
by Th46
.=
(Sum <*u,v*>) + w
by Th45
; verum