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 <*u,w,v*>
let v, u, w be Element of V; :: thesis: Sum <*u,v,w*> = Sum <*u,w,v*>
thus Sum <*u,v,w*> = (u + v) + w by Th46
.= (u + w) + v by Def3
.= Sum <*u,w,v*> by Th46 ; :: thesis: verum