let V be non empty right_complementable Abelian add-associative right_zeroed addLoopStr ; :: thesis: for v being Element of V holds Sum {v} = v

let v be Element of V; :: thesis: Sum {v} = v

A1: Sum <*v*> = v by RLVECT_1:44;

( rng <*v*> = {v} & <*v*> is one-to-one ) by FINSEQ_1:39, FINSEQ_3:93;

hence Sum {v} = v by A1, Def2; :: thesis: verum

let v be Element of V; :: thesis: Sum {v} = v

A1: Sum <*v*> = v by RLVECT_1:44;

( rng <*v*> = {v} & <*v*> is one-to-one ) by FINSEQ_1:39, FINSEQ_3:93;

hence Sum {v} = v by A1, Def2; :: thesis: verum