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