let V be non empty right_complementable Abelian add-associative right_zeroed addLoopStr ; :: thesis: for v, w being Element of V holds
( Sum <*v,(- w)*> = v - w & Sum <*(- w),v*> = v - w )
let v, w be Element of V; :: thesis: ( Sum <*v,(- w)*> = v - w & Sum <*(- w),v*> = v - w )
thus Sum <*v,(- w)*> = v - w by Th45; :: thesis: Sum <*(- w),v*> = v - w
hence Sum <*(- w),v*> = v - w by Th54; :: thesis: verum