let V be non empty right_complementable Abelian add-associative right_zeroed addLoopStr ; :: thesis: for v, u, w being Element of V holds Sum <*u,v,w*> = (Sum <*v,w*>) + u
let v, u, w be Element of V; :: thesis: Sum <*u,v,w*> = (Sum <*v,w*>) + u
thus Sum <*u,v,w*> = (u + v) + w by Th63
.= u + (v + w) by Def6
.= (Sum <*v,w*>) + u by Th62 ; :: thesis: verum